Est-ce que la réduction du déséquilibre de la réponse accroît l’exactitude des estimations de l’enquête ? Section 8. Le deuxième résultat

Dans le résultat 1, les valeurs de la variable étudiée y k MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEamaaBa aaleaacaWGRbaabeaaaaa@3B72@ sont traitées comme étant fixes, non aléatoires. Dans le résultat 2, elles sont aléatoires et leurs propriétés sont précisées par un modèle de régression linéaire ξ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOVdGhaaa@3B1B@ dont les résidus sont ε k = y k x k β MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcaaQaeqyTdu McdaWgaaqcbaAaaiaadUgaaeqaaKaaGkabg2da9iaadMhakmaaBaaa jeaObaGaam4AaaqabaqcaaQaeyOeI0IabCiEayaafaGcdaWgaaqcba AaaiaadUgaaeqaaKaaGkaahk7aaaa@482E@ pour un certain β MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCOSdaaa@3A96@ inconnu :

E ξ ( y k | x k ) = x k β ; E ξ ( ε k 2 | x k ) = σ ε 2 , tout k s ; E ξ ( ε k ε l | x k , x l ) = 0 , tout k l s . ( 8.1 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyramaaBa aaleaacqaH+oaEaeqaaOWaaeWaaeaadaabcaqaaiaadMhadaWgaaWc baGaam4AaaqabaGccaaMc8oacaGLiWoacaaMe8UaaCiEamaaBaaale aacaWGRbaabeaaaOGaayjkaiaawMcaaiabg2da9iqahIhagaqbamaa BaaaleaacaWGRbaabeaakiaaykW7caWHYoGaai4oaiaaywW7caWGfb WaaSbaaSqaaiabe67a4bqabaGcdaqadaqaamaaeiaabaGaeqyTdu2a a0baaSqaaiaadUgaaeaacaaIYaaaaOGaaGPaVdGaayjcSdGaaGjbVl aahIhadaWgaaWcbaGaam4AaaqabaaakiaawIcacaGLPaaacqGH9aqp cqaHdpWCdaqhaaWcbaGaeqyTdugabaGaaGOmaaaakiaacYcacaaMe8 UaaGjbVlaabshacaqGVbGaaeyDaiaabshacaaMe8UaaGjbVlaadUga cqGHiiIZcaWGZbGaai4oaiaaywW7caWGfbWaaSbaaSqaaiabe67a4b qabaGcdaqadaqaamaaeiaabaGaeqyTdu2aaSbaaSqaaiaadUgaaeqa aOGaeqyTdu2aaSbaaSqaaiabloriSbqabaGccaaMc8oacaGLiWoaca aMe8UaaCiEamaaBaaaleaacaWGRbaabeaakiaacYcacaWH4bWaaSba aSqaaiabloriSbqabaaakiaawIcacaGLPaaacqGH9aqpcaaIWaGaai ilaiaaysW7caaMc8UaaeiDaiaab+gacaqG1bGaaeiDaiaaysW7caaM c8Uaam4AaiabgcMi5kabloriSjabgIGiolaadohacaGGUaGaaGzbVl aaywW7caGGOaGaaGioaiaac6cacaaIXaGaaiykaaaa@A1B4@

Les propriétés données en (8.1) s’appliquent également aux unités k MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Aaaaa@3A48@ et l MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeS4eHWgaaa@3A89@ appartenant à tout sous-ensemble r MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaaaa@3A4F@ de s . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Caiaac6 caaaa@3B02@ Le résultat 2 donne l’espérance et la variance approximative de Δ r = ( b r b s ) x ¯ s MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCiLdmaaBa aaleaacaWGYbaabeaakiabg2da9maabmaabaGaaCOyamaaBaaaleaa caWGYbaabeaakiabgkHiTiaahkgadaWgaaWcbaGaam4Caaqabaaaki aawIcacaGLPaaadaahaaWcbeqaaOGamai2gkdiIcaaceWH4bGbaeba daWgaaWcbaGaam4Caaqabaaaaa@48A6@ conditionnellement à un échantillon autopondéré fixe s MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Caaaa@3A50@ et à un ensemble de répondants fixe r MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaaaa@3A4F@ ayant respectivement pour taille n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOBaaaa@3A4B@ et m . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyBaiaac6 caaaa@3AFC@

Résultat 2. Soit s MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Caaaa@3A50@ un échantillon autopondéré de taille n . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOBaiaac6 caaaa@3AFD@ Soit X MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCiwaaaa@3A39@ la matrice des données x MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCiEaaaa@3A59@ de dimensions J × n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOsaiabgE na0kaad6gaaaa@3D31@ dont les colonnes sont x k , MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCiEamaaBa aaleaacaWGRbaabeaakiaacYcaaaa@3C2F@ k s . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4AaiabgI GiolaadohacaGGUaaaaa@3D76@ Alors, sous le modèle ξ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOVdGhaaa@3B1B@ en (8.1),

E ξ ( Δ r | X , r , s ) = 0 ; E ξ ( Δ r 2 | X , r , s ) ( 1 p + I M B p 2 ) σ ε 2 m , ( 8.2 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyramaaBa aaleaacqaH+oaEaeqaaOWaaeWaaeaadaabcaqaaiabfs5aenaaBaaa leaacaWGYbaabeaakiaaykW7aiaawIa7aiaaysW7caWHybGaaiilai aadkhacaGGSaGaam4CaaGaayjkaiaawMcaaiabg2da9iaaicdacaGG 7aGaaGzbVlaadweadaWgaaWcbaGaeqOVdGhabeaakmaabmaabaWaaq GaaeaacqqHuoardaqhaaWcbaGaamOCaaqaaiaaikdaaaGccaaMc8oa caGLiWoacaaMe8UaaCiwaiaacYcacaWGYbGaaiilaiaadohaaiaawI cacaGLPaaacqGHijYUdaqadaqaaiaaigdacqGHsislcaWGWbGaey4k aSYaaSaaaeaacaWGjbGaamytaiaadkeaaeaacaWGWbWaaWbaaSqabe aacaaIYaaaaaaaaOGaayjkaiaawMcaamaalaaabaGaeq4Wdm3aa0ba aSqaaiabew7aLbqaaiaaikdaaaaakeaacaWGTbaaaiaacYcacaaMf8 UaaGzbVlaaywW7caaMf8UaaGzbVlaacIcacaaI4aGaaiOlaiaaikda caGGPaaaaa@7A11@

m MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyBaaaa@3A4A@ est la taille de l’ensemble de répondants fixe r , MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaiaacY caaaa@3AFF@ p = m / n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiCaiabg2 da9maalyaabaGaamyBaaqaaiaad6gaaaaaaa@3D4E@ est le taux de réponse et I M B MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbaaaa@3BBF@ est donné par (3.2).

Le résultat 2 (pour un vecteur x MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCiEaaaa@3A59@ arbitraire et les y k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEamaaBa aaleaacaWGRbaabeaaaaa@3B71@ aléatoires) reflète le résultat 1 (pour le vecteur x MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCiEaaaa@3A59@ de groupes et les y k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEamaaBa aaleaacaWGRbaabeaaaaa@3B71@ non aléatoires) en ce sens que l’un et l’autre donnent une moyenne conditionnelle nulle et la même forme linéairement croissante pour la variance conditionnelle approximative.

Le calcul du résultat 2 donné à l’annexe 3 s’appuie sur une comparaison de deux formes quadratiques en x ¯ r x ¯ s MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabCiEayaara WaaSbaaSqaaiaadkhaaeqaaOGaeyOeI0IabCiEayaaraWaaSbaaSqa aiaadohaaeqaaaaa@3EC8@ données dans (3.1), Q s MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyuamaaBa aaleaacaWGZbaabeaaaaa@3B52@ et Q r . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyuamaaBa aaleaacaWGYbaabeaakiaac6caaaa@3C0D@ La première est utilisée dans la statistique de déséquilibre (3.2), I M B = P 2 Q s ; MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaad2 eacaWGcbGaeyypa0JaamiuamaaCaaaleqabaGaaGOmaaaakiaadgfa daWgaaWcbaGaam4CaaqabaGccaGG7aaaaa@4150@ la seconde détermine les facteurs de pondération g k MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcaaMaam4zaO WaaSbaaKqaGfaacaWGRbaabeaaaaa@3C32@ pour l’estimateur CAL (5.1). L’approximation Q r Q s , MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpD0xh9Wqpm0db9Wq pepeuf0xe9q8qiYRWFGCk9vi=dbvc9s8vr0db9Fn0dbbG8Fq0Jfr=x fr=xfbpdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyuamaaBa aaleaacaWGYbaabeaakiabgIKi7kaadgfadaWgaaWcbaGaam4Caaqa baGccaGGSaaaaa@3FC0@ nécessaire pour le résultat 2, est justifiée à l’annexe 2.

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