Est-ce que la réduction du déséquilibre de la réponse accroît l’exactitude des estimations de l’enquête ? Section 9. Essai empirique

Les résultats 1 et 2 donnent le fondement pour tester empiriquement à la présente section la façon dont la moyenne et la variance de l’écart Y ^ C A L Y ^ F U L = N ^ Δ r = N ^ ( b r b s ) x ¯ s MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmywayaaja WaaSbaaSqaaiaadoeacaWGbbGaamitaaqabaGccqGHsislceWGzbGb aKaadaWgaaWcbaGaamOraiaadwfacaWGmbaabeaakiabg2da9iqad6 eagaqcaiabfs5aenaaBaaaleaacaWGYbaabeaakiabg2da9iqad6ea gaqcamaabmaabaGaaCOyamaaBaaaleaacaWGYbaabeaakiabgkHiTi aahkgadaWgaaWcbaGaam4CaaqabaaakiaawIcacaGLPaaadaahaaWc beqaaOGamai2gkdiIcaaceWH4bGbaebadaWgaaWcbaGaam4Caaqaba aaaa@53C2@ dépendent du déséquilibre I M B . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbGaaiOlaaaa@3C71@ Les deux résultats énoncent que la variance de Δ r MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCiLdmaaBa aaleaacaWGYbaabeaaaaa@3B9B@ augmente de manière à peu près linéaire à mesure que I M B MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbaaaa@3BBF@ augmente, sans être faible, même si I M B MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbaaaa@3BBF@  est proche de zéro.

Nous utilisons des données réelles provenant d’une enquête estonienne réalisée auprès de 17 540 ménages. Les variables qui suivent sont disponibles pour chaque ménage, à savoir le revenu net du ménage, utilisé ici comme variable étudiée y , MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacY caaaa@3B06@ et trois variables catégoriques se rapportant au chef de ménage désigné, utilisées ici comme variables auxiliaires : i) sexe (1 pour masculin, 0 pour féminin), ii) activité économique (1 pour occupé, 0 pour non occupé) et iii)études, avec trois niveaux exhaustifs : faible, moyen et élevé.

Nous calculons la moyenne Δ ¯ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafuiLdqKbae baaaa@3AD6@ de Δ r MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCiLdmaaBa aaleaacaWGYbaabeaaaaa@3B9B@ et la variance S Δ 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaDa aaleaacqqHuoaraeaacaaIYaaaaaaa@3C7F@ de Δ r MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCiLdmaaBa aaleaacaWGYbaabeaaaaa@3B9B@ en prenant la moyenne sur les ensembles r pour une moyenne x ¯ r MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabCiEayaara WaaSbaaSqaaiaadkhaaeqaaaaa@3B94@ fixe, sachant s . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Caiaac6 caaaa@3B02@

9.1 Situation de test 1

En harmonie avec le résultat 1, nous voulons prendre en considération les ensembles de réponses r MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaaaa@3A4F@ de taille fixe m MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyBaaaa@3A4A@ issus de l’échantillon s MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Caaaa@3A50@ de taille n . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOBaiaac6 caaaa@3AFD@ Le volume des calculs est prohibitif, même pour une valeur assez faible de n . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOBaiaac6 caaaa@3AFD@ Nous avons tiré s MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Caaaa@3A50@ comme un échantillon aléatoire simple de taille n = 20 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOBaiabg2 da9iaaikdacaaIWaaaaa@3CC7@ parmi une population de 17 540. Les d k MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaBa aaleaacaWGRbaabeaaaaa@3B5D@ sont alors constants. La moyenne d’échantillon de la variable y MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaaaa@3A56@ (revenu du ménage) était y ¯ s = 10 386 , 65. MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyEayaara WaaSbaaSqaaiaadohaaeqaaOGaeyypa0JaaGymaiaaicdacaaMe8Ua aG4maiaaiIdacaaI2aGaaiilaiaaiAdacaaI1aGaaiOlaaaa@44C4@ Nous définissons x k MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCiEamaaBa aaleaacaWGRbaabeaaaaa@3B75@ comme étant le vecteur de groupes de dimension J = 3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOsaiabg2 da9iaaiodaaaa@3BEA@ qui précise les trois niveaux d’études exhaustifs, à savoir faible, moyen et élevé. Pour l’échantillon réalisé s , MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4CaiaacY caaaa@3B00@ nous avons n x ¯ s = ( 5 , 8 , 7 ) . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOBaiqahI hagaqeamaaBaaaleaacaWGZbaabeaakiabg2da9maabmaabaGaaGyn aiaacYcacaaI4aGaaiilaiaaiEdaaiaawIcacaGLPaaadaahaaWcbe qaaOGamai2gkdiIcaacaGGUaaaaa@468C@

Nous avons fixé la taille des ensembles de réponses r MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaaaa@3A4F@ à m = 12. MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyBaiabg2 da9iaaigdacaaIYaGaaiOlaaaa@3D79@ Le taux de réponse est de 60 % pour chacun des ( 20 12 ) 1 , 26 × 10 5 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaafa qabeGabaaabaqcLbqacaaIYaGaaGimaaGcbaqcLbqacaaIXaGaaGOm aaaaaOGaayjkaiaawMcaaiabgIKi7kaaigdacaGGSaGaaGOmaiaaiA dacqGHxdaTcaaIXaGaaGimamaaCaaaleqabaGaaGynaaaaaaa@47DD@ ensembles de réponses r MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaaaa@3A4F@ possibles. De ceux-ci, nous avons exclu tous ceux pour lesquels le vecteur des nombres de réponses m x ¯ r MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyBaiqahI hagaqeamaaBaaaleaacaWGYbaabeaaaaa@3C86@ contenait un zéro, pour éviter une matrice Σ r MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcaaMaaC4OdO WaaSbaaSqaaiaadkhaaeqaaaaa@3C1D@ singulière. Cela nous a laissé 31 configurations ( m 1 , m 2 , m 3 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaaca WGTbWaaSbaaSqaaiaaigdaaeqaaOGaaiilaiaad2gadaWgaaWcbaGa aGOmaaqabaGccaGGSaGaamyBamaaBaaaleaacaaIZaaabeaaaOGaay jkaiaawMcaaaaa@41ED@ telles que m 1 + m 2 + m 3 = 12 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyBamaaBa aaleaacaaIXaaabeaakiabgUcaRiaad2gadaWgaaWcbaGaaGOmaaqa baGccqGHRaWkcaWGTbWaaSbaaSqaaiaaiodaaeqaaOGaeyypa0JaaG ymaiaaikdaaaa@4345@ et les trois nombres m j 1. MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcaaMaamyBaO WaaSbaaKqaGfaacaWGQbaabeaajaaycqGHLjYScaaIXaGaaiOlaaaa @3FD3@ Pour chacune des 31 possibilités, nous avons calculé Δ ¯ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafuiLdqKbae baaaa@3AD6@ et S Δ 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaDa aaleaacqqHuoaraeaacaaIYaaaaaaa@3C7F@ en prenant la moyenne sur les ensembles de réponses r MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaaaa@3A4F@ satisfaisant la configuration fixe. Par exemple, ( m 1 , m 2 , m 3 ) = ( 3 , 4 , 5 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaaca WGTbWaaSbaaSqaaiaaigdaaeqaaOGaaiilaiaad2gadaWgaaWcbaGa aGOmaaqabaGccaGGSaGaamyBamaaBaaaleaacaaIZaaabeaaaOGaay jkaiaawMcaaiabg2da9maabmaabaGaaG4maiaacYcacaaI0aGaaiil aiaaiwdaaiaawIcacaGLPaaaaaa@4816@ est satisfaite par 14 700 ensembles de réponses r , MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaiaacY caaaa@3AFF@ de sorte que la moyenne et la variance de Δ r MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcaaMaeuiLdq KcdaWgaaWcbaGaamOCaaqabaaaaa@3C54@ sont calculées sur ces ensembles. D’autres configurations donnent un nombre beaucoup plus faible d’ensembles de réponses, par exemple, seulement 70 pour la configuration (3, 8, 1); quelques-unes de ces configurations peuvent être très influentes dans les calculs. Pour chacun des 31 cas, Δ ¯ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafuiLdqKbae baaaa@3AD6@ est théoriquement nulle, en vertu du résultat 1. Les calculs l’ont confirmé; une représentation graphique de Δ ¯ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafuiLdqKbae baaaa@3AD6@ en fonction de I M B MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbaaaa@3BBF@ n’est pas nécessaire. La figure 9.1 montre le tracé des 31 points de S Δ 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaDa aaleaacqqHuoaraeaacaaIYaaaaaaa@3C7F@ en fonction de I M B . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbGaaiOlaaaa@3C71@ En raison du caractère non unique de I M B MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbaaaa@3BBF@ mentionné plus haut, il arrive plusieurs fois que plus d’une valeur de S Δ 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaDa aaleaacqqHuoaraeaacaaIYaaaaaaa@3C7F@ existe pour une même valeur I M B . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbGaaiOlaaaa@3C71@ La figure 9.1 montre que S Δ 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaDa aaleaacqqHuoaraeaacaaIYaaaaaaa@3C7F@ suit clairement une tendance à la hausse quand I M B MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbaaaa@3BBF@ augmente. La figure 9.1 montre aussi l’approximation S Δ 2 S Δ a p p r o x 2 = ( S y 2 / m ) ( 1 p + I M B / p 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaDa aaleaacqqHuoaraeaacaqGYaaaaOGaeyisISRaam4uamaaDaaaleaa cqqHuoarcaWGHbGaamiCaiaadchacaWGYbGaam4BaiaadIhaaeaaca aIYaaaaOGaeyypa0ZaaeWaaeaadaWcgaqaaKaaGjaadofakmaaDaaa jeaybaGaamyEaaqaaiaaikdaaaaakeaajaaycaWGTbaaaaGccaGLOa GaayzkaaWaaeWaaeaajaaycaaIXaGaeyOeI0IaamiCaiabgUcaROWa aSGbaeaacaWGjbGaamytaiaadkeaaeaajaaycaWGWbGcdaahaaqcba wabeaacaaIYaaaaaaaaOGaayjkaiaawMcaaaaa@5973@ issue du résultat 1. Nous avons p = 0 , 6 ; m = 12 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiCaiabg2 da9iaaicdacaGGSaGaaGOnaiaacYcacaaMe8UaamyBaiabg2da9iaa igdacaaIYaaaaa@4329@ et S y 2 = 26 , 3 × 10 6 , MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaDa aaleaacaWG5baabaGaaGOmaaaakiabg2da9iaaikdacaaI2aGaaiil aiaaiodacqGHxdaTcaaIXaGaaGimamaaCaaaleqabaGaaGOnaaaaki aacYcaaaa@4543@ de sorte que l’approximation calculée, linéaire en I M B , MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbGaaiilaaaa@3C6F@ est S Δ a p p r o x 2 = a + b I M B MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaDa aaleaacqqHuoarcaWGHbGaamiCaiaadchacaWGYbGaam4BaiaadIha aeaacaqGYaaaaOGaeyypa0JaamyyaiabgUcaRiaadkgacaaMe8Uaam ysaiaad2eacaWGcbaaaa@49E3@ avec a = 0 , 879 × 10 6 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyyaiabg2 da9iaaicdacaGGSaGaaGioaiaaiEdacaaI5aGaey41aqRaaGymaiaa icdadaahaaWcbeqaaiaaiAdaaaaaaa@436D@ et b = 6 , 102 × 10 6 . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOyaiabg2 da9iaaiAdacaGGSaGaaGymaiaaicdacaaIYaGaey41aqRaaGymaiaa icdadaahaaWcbeqaaiaaiAdaaaGccaGGUaaaaa@441B@ Pour les points associés à une faible valeur I M B , MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbGaaiilaaaa@3C6F@ S Δ 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaDa aaleaacqqHuoaraeaacaaIYaaaaaaa@3C7F@ concorde étroitement avec S Δ a p p r o x 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaDa aaleaacqqHuoarcaWGHbGaamiCaiaadchacaWGYbGaam4BaiaadIha aeaacaqGYaaaaaaa@4230@ linéairement croissante. L’une des raisons est que, si I M B MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbaaaa@3BBF@ est faible, les taux de réponse de groupe p j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiCamaaBa aaleaacaWGQbaabeaaaaa@3B68@ varient peu, ce qui est une des conditions pour une approximation proche, comme l’explique le calcul du résultat 1 à l’annexe 1. Pour des valeurs plus élevées de I M B , MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbGaaiilaaaa@3C6F@ la tendance à la hausse en S Δ 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaDa aaleaacqqHuoaraeaacaaIYaaaaaaa@3C7F@ demeure évidente, mais la dispersion autour de la ligne droite théorique est plus prononcée. Cinq points aberrants dans la figure 9.1 ont une très grande valeur de S Δ 2 ; MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaDa aaleaacqqHuoaraeaacaaIYaaaaOGaai4oaaaa@3D48@ trois d’entre eux sont obtenus quand une composante de ( m 1 , m 2 , m 3 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaaca WGTbWaaSbaaSqaaiaaigdaaeqaaOGaaiilaiaad2gadaWgaaWcbaGa aGOmaaqabaGccaGGSaGaamyBamaaBaaaleaacaaIZaaabeaaaOGaay jkaiaawMcaaaaa@41ED@ est égale au nombre maximal (5 ou 8 ou 7). Pour ces points, l’on s’attend à une approximation linéaire moins précise, les p j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiCamaaBa aaleaacaWGQbaabeaaaaa@3B68@ étant loin d’être égaux.

Figure 9.1 de l'article Est-ce que la réduction du déséquilibre de la réponse accroît l’exactitude des estimations de l’enquête ?

Description de la figure 9.1

En utilisant des données de la situation de test 1, ce graphique présente le nuage de points de la variance conditionnelle de Δ r MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrpK0dXde9LqFHe9Lq pepeea0xd9q8qiYRWxGi6xij=dbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meqabeqadiWaceGabeqabeWabeqaeeaakeaacaWHuoWaaS baaSqaaiaadkhaaeqaaaaa@39F6@  sur l’axe des y allant de 0 à 6× 10 6 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpK0dXde9LqFHe9Lq pepeea0xd9q8qiYRWxGi6xij=dbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaaI2aGaey 41aqRaaGymaiaaicdadaahaaWcbeqaaiabgkHiTiaaiAdaaaaaaa@3DDF@ en fonction du déséquilibre IMB MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbaaaa@3BC0@  allant de 0 à approximativement 0,17 sur l’axe des x. Le graphique inclut une approximation linéaire du nuage de point tel que décrit dans le texte. Cinq valeurs aberrantes avec des valeurs de x >0,10 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpK0dXde9LqFHe9Lq pepeea0xd9q8qiYRWxGi6xij=dbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqGH+aGpca qGWaGaaeilaiaabgdacaqGWaaaaa@3B8A@  et y >3× 10 6 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpK0dXde9LqFHe9Lq pepeea0xd9q8qiYRWxGi6xij=dbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqGH+aGpca aIZaGaey41aqRaaGymaiaaicdadaahaaWcbeqaaiabgkHiTiaaiAda aaaaaa@3EE4@  sont visibles.

9.2 Situation de test 2

La configuration et les étapes de calcul sont similaires à celles de la situation de test 1, mais x k MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCiEamaaBa aaleaacaWGRbaabeaaaaa@3B75@ n’est plus un vecteur de groupes; certains résultats changent considérablement comparativement à la situation de test 1.

Un nouvel échantillon aléatoire simple s MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Caaaa@3A50@ de taille n = 20 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOBaiabg2 da9iaaikdacaaIWaaaaa@3CC7@ a été tiré parmi les 17 540 ménages. Pour cet échantillon, y ¯ s = 9 618,4 . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyEayaara WaaSbaaSqaaiaadohaaeqaaOGaeyypa0JaaeyoaiaaysW7caqG2aGa aeymaiaabIdacaqGSaGaaeinaiaac6caaaa@432B@ Posons que x k MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCiEamaaBa aaleaacaWGRbaabeaaaaa@3B75@ englobe les trois variables auxiliaires (i), (ii) et (iii), mais que celles-ci ne sont pas entièrement croisées : sexe (variable univariée codée 0 ou 1), activité économique (variable univariée codée 0 ou 1) et niveau d’études (trois catégories exhaustives codées (1,0,0) ou (0,1,0) ou (0,0,1)). x k MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCiEamaaBa aaleaacaWGRbaabeaaaaa@3B75@ n’est pas un vecteur de groupes; sa dimension est de 1 + 1 + 3 = 5 , MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiabgU caRiaaigdacqGHRaWkcaaIZaGaeyypa0JaaGynaiaacYcaaaa@3FC4@ et x r MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCiEamaaBa aaleaacaWGYbaabeaaaaa@3B7C@ possède 2 × 2 × 3 = 12 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGOmaiabgE na0kaaikdacqGHxdaTcaaIZaGaeyypa0JaaGymaiaaikdaaaa@4238@ valeurs possibles Σ r MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcaaMaaC4OdO WaaSbaaSqaaiaadkhaaeqaaaaa@3C1D@ et Σ s MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcaaMaaC4OdO WaaSbaaSqaaiaadohaaeqaaaaa@3C1E@ ne sont pas des matrices diagonales. Nous avons n x ¯ s = ( 9 , 11 , 4 , 7 , 9 ) . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOBaiqahI hagaqeamaaBaaaleaacaWGZbaabeaakiabg2da9maabmaabaGaaGyo aiaacYcacaaIXaGaaGymaiaacYcacaaI0aGaaiilaiaaiEdacaGGSa GaaGyoaaGaayjkaiaawMcaamaaCaaaleqabaGccWaGyBOmGikaaiaa c6caaaa@4A25@ Pour cet échantillon s , MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4CaiaacY caaaa@3B00@ nous avons considéré les ensembles de réponses r MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaaaa@3A4F@ de taille fixe m = 12 , MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyBaiabg2 da9iaaigdacaaIYaGaaiilaaaa@3D77@ sauf ceux pour lesquels une ou plusieurs des cinq composantes du vecteur des nombres de réponses m x ¯ r MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyBaiqahI hagaqeamaaBaaaleaacaWGYbaabeaaaaa@3C86@ sont nulles. Cela a laissé 658 vecteurs différents m x ¯ r , MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyBaiqahI hagaqeamaaBaaaleaacaWGYbaabeaakiaacYcaaaa@3D40@ chacun composé de cinq nombres non nuls et satisfait par un certain nombre d’ensembles de réponses r MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaaaa@3A4F@ sur lesquels nous avons calculé, en prenant la moyenne, le terme Δ ¯ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafuiLdqKbae baaaa@3AD6@ et la variance S Δ 2 . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaDa aaleaacqqHuoaraeaacaqGYaaaaOGaaiOlaaaa@3D34@ Il s’agit donc de moments conditionnés sur x ¯ r . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabCiEayaara WaaSbaaSqaaiaadkhaaeqaaOGaaiOlaaaa@3C50@

La figure 9.2 montre le tracé des 658 points pour Δ ¯ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafuiLdqKbae baaaa@3AD6@ en fonction de I M B . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbGaaiOlaaaa@3C71@ Dans la situation de test 1, Δ ¯ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafuiLdqKbae baaaa@3AD6@ était nulle pour chaque point parce que x k MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCiEamaaBa aaleaacaWGRbaabeaaaaa@3B75@ était un vecteur de groupes. Ce n’est pas le cas dans la figure 9.2, où les moyennes Δ ¯ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafuiLdqKbae baaaa@3AD6@ s’étalent en éventail quand I M B MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbaaaa@3BBF@ augmente. Elles sont nettement plus concentrées autour de zéro pour les faibles valeurs que pour les grandes valeurs de I M B . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbGaaiOlaaaa@3C71@ Plusieurs points (c’est-à-dire plusieurs moyennes x ¯ r ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeGaaeaace WH4bGbaebadaWgaaWcbaGaamOCaaqabaaakiaawMcaaaaa@3C66@ peuvent donner la même ou quasi la même valeur de I M B . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbGaaiOlaaaa@3C71@ La figure 9.2 montre que dans un voisinage restreint d’une valeur fixe I M B 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbWaaSbaaSqaaiaaicdaaeqaaaaa@3CA5@ sur l’axe I M B , MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbGaaiilaaaa@3C6F@ la moyenne des moyennes Δ ¯ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafuiLdqKbae baaaa@3AD6@ est approximativement nulle. En référence au résultat 2, nous pouvons nous attendre à ce que la moyenne de Δ ¯ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafuiLdqKbae baaaa@3AD6@ pour une valeur fixe de I M B MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbaaaa@3BBF@ soit quasi nulle : sous le modèle (8.1) pour y k , MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEamaaBa aaleaacaWGRbaabeaakiaacYcaaaa@3C2C@ le résultat 2 dit que E ξ ( Δ r | X , r , s ) = 0. MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyramaaBa aaleaacqaH+oaEaeqaaOWaaeWaaeaadaabcaqaaiabfs5aenaaBaaa leaacaWGYbaabeaakiaaykW7aiaawIa7aiaaysW7caWHybGaaiilai aadkhacaGGSaGaam4CaaGaayjkaiaawMcaaiabg2da9iaaicdacaGG Uaaaaa@4B87@ Quand X MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCiwaaaa@3A39@ et r MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaaaa@3A4F@ sont fixes, il en est de même de I M B . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbGaaiOlaaaa@3C71@ Si le modèle est une raisonnablement bonne représentation, la moyenne de Δ r MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdq0aaS baaSqaaiaadkhaaeqaaaaa@3BE1@ pour un I M B MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbaaaa@3BBF@ fixe devrait être proche de zéro, comme l’indique la figure 9.2.

La figure 9.3 montre le tracé de la variance conditionnelle S Δ 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaDa aaleaacqqHuoaraeaacaaIYaaaaaaa@3C7F@ en fonction de I M B . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbGaaiOlaaaa@3C71@ La tendance d’une variance S Δ 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaDa aaleaacqqHuoaraeaacaaIYaaaaaaa@3C7F@ linéairement croissante en I M B MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbaaaa@3BBF@ prédomine, même si x k MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCiEamaaBa aaleaacaWGRbaabeaaaaa@3B75@ n’est pas un vecteur de groupes ici. La figure 9.3 montre la droite approximative calculée S Δ a p p r o x 2 = ( σ ^ ε 2 / m ) ( 1 p + I M B / p 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaDa aaleaacqqHuoarcaWGHbGaamiCaiaadchacaWGYbGaam4BaiaadIha aeaacaaIYaaaaOGaeyypa0ZaaeWaaeaadaWcgaqaaKaaGjqbeo8aZz aajaGcdaqhaaqcbawaaiabew7aLbqaaiaaikdaaaaakeaacaWGTbaa aaGaayjkaiaawMcaamaabmaabaqcaaMaaGymaiabgkHiTiaadchacq GHRaWkkmaalyaabaGaamysaiaad2eacaWGcbaabaqcaaMaamiCaOWa aWbaaKqaGfqabaGaaGOmaaaaaaaakiaawIcacaGLPaaaaaa@55C9@ dérivée du résultat 2, en utilisant σ ^ ε 2 = s ( y k x k b s ) 2 / ( n J ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafq4WdmNbaK aadaqhaaWcbaGaeqyTdugabaGaaGOmaaaakiabg2da9maalyaabaWa aabeaeaadaqadaqaaiaadMhadaWgaaWcbaGaam4AaaqabaGccqGHsi slceWH4bGbauaadaWgaaWcbaGaam4AaaqabaGccaWHIbWaaSbaaSqa aiaadohaaeqaaaGccaGLOaGaayzkaaWaaWbaaSqabeaacaaIYaaaaa qaaiaadohaaeqaniabggHiLdaakeaadaqadaqaaiaad6gacqGHsisl caWGkbaacaGLOaGaayzkaaaaaaaa@4FC2@ pour estimer σ ε 2 . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aa0 baaSqaaiabew7aLbqaaiaaikdaaaGccaGGUaaaaa@3E67@ Nous avons J = 5 , p = 0 , 6 ; MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOsaiabg2 da9iaaiwdacaGGSaGaaGjbVlaadchacqGH9aqpcaaIWaGaaiilaiaa iAdacaGGSaaaaa@42FE@ m = 12 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyBaiabg2 da9iaaigdacaaIYaaaaa@3CC7@ et σ ^ ε 2 = 33 , 6 × 10 6 , MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafq4WdmNbaK aadaqhaaWcbaGaeqyTdugabaGaaGOmaaaakiabg2da9iaaiodacaaI ZaGaaiilaiaaiAdacqGHxdaTcaaIXaGaaGimamaaCaaaleqabaGaaG OnaaaakiaacYcaaaa@46E8@ de sorte que la droite dans la figure 9.3 est S Δ a p p r o x 2 = a + b I M B MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaDa aaleaacqqHuoarcaWGHbGaamiCaiaadchacaWGYbGaam4BaiaadIha aeaacaqGYaaaaOGaaGzaVlabg2da9iaadggacqGHRaWkcaWGIbGaaG jbVlaadMeacaWGnbGaamOqaaaa@4B6D@ avec a = 1 , 12 × 10 6 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyyaiabg2 da9iaaigdacaGGSaGaaGymaiaaikdacqGHxdaTcaaIXaGaaGimamaa CaaaleqabaGaaGOnaaaaaaa@429F@ et b = 7 , 78 × 10 6 . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOyaiabg2 da9iaaiEdacaGGSaGaaG4naiaaiIdacqGHxdaTcaaIXaGaaGimamaa CaaaleqabaGaaGOnaaaakiaac6caaaa@436E@ L’approximation linéaire tient particulièrement bien pour une faible valeur de I M B , MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbGaaiilaaaa@3C6F@ disons inférieure à 0,1. Pour les grandes valeurs de I M B , MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbGaaiilaaaa@3C6F@ la dispersion est importante; S Δ 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaDa aaleaacqqHuoaraeaacaaIYaaaaaaa@3C7F@ prend certaines valeurs très grandes, et certaines valeurs très faibles également. La figure 9.4 montre le comportement conjoint de Δ ¯ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafuiLdqKbae baaaa@3AD6@ et S Δ 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaDa aaleaacqqHuoaraeaacaaIYaaaaaaa@3C7F@ pour les 658 points. La taille d’un point est proportionnelle à I M B 2 ; MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbWaaWbaaSqabeaacaaIYaaaaOGaai4oaaaa@3D71@ l’élévation au carré a pour objet de mieux contraster les grandes et les petites valeurs de I M B . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbGaaiOlaaaa@3C71@ Nous constatons que les ensembles de réponses r MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaaaa@3A4F@ pour lesquels I M B MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbaaaa@3BBF@ est petit donnent de faibles valeurs de Δ ¯ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafuiLdqKbae baaaa@3AD6@ et S Δ 2 , MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaDa aaleaacqqHuoaraeaacaaIYaaaaOGaaiilaaaa@3D39@ signe favorable car les estimateurs CAL et FUL sont alors proches. Par exemple, pour les points satisfaisant I M B 0 , 1 ; MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbGaeyizImQaaGimaiaacYcacaaIXaGaaiilaaaa@4049@ Δ ¯ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafuiLdqKbae baaaa@3AD6@ est dans l’intervalle (-1 390; 1 447) et S Δ 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaDa aaleaacqqHuoaraeaacaaIYaaaaaaa@3C7F@ est dans (0,846×106; 4,86×106). Ces intervalles sont étroits; cela est encore plus prononcé pour I M B 0 , 05. MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbGaeyizImQaaGimaiaacYcacaaIWaGaaGynaiaac6caaaa@4109@ Quand I M B MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbaaaa@3BBF@ est grand, cette situation avantageuse disparaît. Par exemple, Δ ¯ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafuiLdqKbae baaaa@3AD6@ peut être très petite et, simultanément, S Δ 2 , MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaDa aaleaacqqHuoaraeaacaaIYaaaaOGaaiilaaaa@3D39@ très grande (points au milieu et du côté droit de la figure). Par ailleurs, S Δ 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaDa aaleaacqqHuoaraeaacaaIYaaaaaaa@3C7F@ peut être quasi nulle tandis que Δ ¯ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafuiLdqKbae baaaa@3AD6@ est très grande en valeur absolue (points dans les parties supérieure et inférieure gauche de la figure.) La situation de test 2 illustre le fait qu’un vecteur sans groupes x k MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCiEamaaBa aaleaacaWGRbaabeaaaaa@3B75@ peut donner à la fois une moyenne distinctement non nulle de Δ r MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqKaaG PaVpaaBaaaleaacaWGYbaabeaaaaa@3D6C@ et une variance élevée de Δ r , MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdq0aaS baaSqaaiaadkhaaeqaaOGaaiilaaaa@3C9B@ et que ces tendances sont accentuées par un grand déséquilibre.

Figure 9.2 de l'article Est-ce que la réduction du déséquilibre de la réponse accroît l’exactitude des estimations de l’enquête ?

Description de la figure 9.2

En utilisant des données de la situation de test 2, ce graphique présente le nuage de points de la moyenne conditionnelle de Δ r MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrpK0dXde9LqFHe9Lq pepeea0xd9q8qiYRWxGi6xij=dbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meqabeqadiWaceGabeqabeWabeqaeeaakeaacaWHuoWaaS baaSqaaiaadkhaaeqaaaaa@39F6@  sur l’axe des y allant de 4× 10 6 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpK0dXde9LqFHe9Lq pepeea0xd9q8qiYRWxGi6xij=dbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqGHsislca aI0aGaey41aqRaaGymaiaaicdadaahaaWcbeqaaiabgkHiTiaaiAda aaaaaa@3ECA@  à 4× 10 6 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpK0dXde9LqFHe9Lq pepeea0xd9q8qiYRWxGi6xij=dbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaaI0aGaey 41aqRaaGymaiaaicdadaahaaWcbeqaaiabgkHiTiaaiAdaaaaaaa@3DDD@  en fonction du déséquilibre IMB MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbaaaa@3BC0@  allant de 0 à approximativement 0,22 sur l’axe des x. Les données y sont centrées sur 0 mais s’étalent en éventail alors que les valeurs de x augmentent.

Figure 9.3 de l'article Est-ce que la réduction du déséquilibre de la réponse accroît l’exactitude des estimations de l’enquête ?

Description de la figure 9.3

En utilisant des données de la situation de test 2, ce graphique présente le nuage de points de la variance conditionnelle de Δ r MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrpK0dXde9LqFHe9Lq pepeea0xd9q8qiYRWxGi6xij=dbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meqabeqadiWaceGabeqabeWabeqaeeaakeaacaWHuoWaaS baaSqaaiaadkhaaeqaaaaa@39F6@  sur l’axe des y allant de 0 à 15× 10 6 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpK0dXde9LqFHe9Lq pepeea0xd9q8qiYRWxGi6xij=dbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaaIXaGaaG ynaiabgEna0kaaigdacaaIWaWaaWbaaSqabeaacqGHsislcaaI2aaa aaaa@3E99@  en fonction du déséquilibre IMB MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbaaaa@3BC0@  allant de 0 à approximativement 0,22 sur l’axe des x. Le patron prédominant est celui d’une variance qui s’étale en éventail asymétrique et croît linéairement selon IMB. MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbGaaiOlaaaa@3C72@

Figure 9.4 de l'article Est-ce que la réduction du déséquilibre de la réponse accroît l’exactitude des estimations de l’enquête ?

Description de la figure 9.4

En utilisant des données de la situation de test 2, ce graphique présente le nuage de points de la moyenne conditionnelle de Δ r MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrpK0dXde9LqFHe9Lq pepeea0xd9q8qiYRWxGi6xij=dbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meqabeqadiWaceGabeqabeWabeqaeeaakeaacaWHuoWaaS baaSqaaiaadkhaaeqaaaaa@39F6@  sur l’axe des y allant de 5× 10 6 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpK0dXde9LqFHe9Lq pepeea0xd9q8qiYRWxGi6xij=dbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqGHsislca aI1aGaey41aqRaaGymaiaaicdadaahaaWcbeqaaiabgkHiTiaaiAda aaaaaa@3ECB@  à 5× 10 6 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpK0dXde9LqFHe9Lq pepeea0xd9q8qiYRWxGi6xij=dbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaaI1aGaey 41aqRaaGymaiaaicdadaahaaWcbeqaaiabgkHiTiaaiAdaaaaaaa@3DDE@  en fonction de la variance conditionnelle de Δ r MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrpK0dXde9LqFHe9Lq pepeea0xd9q8qiYRWxGi6xij=dbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meqabeqadiWaceGabeqabeWabeqaeeaakeaacaWHuoWaaS baaSqaaiaadkhaaeqaaaaa@39F6@  allant de 0 à 16× 10 6 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpK0dXde9LqFHe9Lq pepeea0xd9q8qiYRWxGi6xij=dbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaaIXaGaaG OnaiabgEna0kaaigdacaaIWaWaaWbaaSqabeaacqGHsislcaaI2aaa aaaa@3E9A@  sur l’axe des x. La taille des points est proportionnelle à IM B 2 ; MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbWaaWbaaSqabeaacaaIYaaaaOGaai4oaaaa@3D72@  on constate que pour un déséquilibre élevé, il peut y avoir une moyenne très petite et, simultanément, une variance très grande (points au milieu et du côté droit de la figure). Par ailleurs, la variance peut être quasi nulle tandis que la moyenne est très grande en valeur absolue (points dans les parties supérieure et inférieure gauche de la figure.)

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