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- Articles and reports: 12-001-X201000211376Description:
This article develops computational tools, called indicators, for judging the effectiveness of the auxiliary information used to control nonresponse bias in survey estimates, obtained in this article by calibration. This work is motivated by the survey environment in a number of countries, notably in northern Europe, where many potential auxiliary variables are derived from reliable administrative registers for household and individuals. Many auxiliary vectors can be composed. There is a need to compare these vectors to assess their potential for reducing bias. The indicators in this article are designed to meet that need. They are used in surveys at Statistics Sweden. General survey conditions are considered: There is probability sampling from the finite population, by an arbitrary sampling design; nonresponse occurs. The probability of inclusion in the sample is known for each population unit; the probability of response is unknown, causing bias. The study variable (the y-variable) is observed for the set of respondents only. No matter what auxiliary vector is used in a calibration estimator (or in any other estimation method), a residual bias will always remain. The choice of a "best possible" auxiliary vector is guided by the indicators proposed in the article. Their background and computational features are described in the early sections of the article. Their theoretical background is explained. The concluding sections are devoted to empirical studies. One of these illustrates the selection of auxiliary variables in a survey at Statistics Sweden. A second empirical illustration is a simulation with a constructed finite population; a number of potential auxiliary vectors are ranked in order of preference with the aid of the indicators.
Release date: 2010-12-21 - Articles and reports: 12-001-X201000211377Description:
We consider the problem of parameter estimation with auxiliary information, where the auxiliary information takes the form of known moments. Calibration estimation is a typical example of using the moment conditions in sample surveys. Given the parametric form of the original distribution of the sample observations, we use the estimated importance sampling of Henmi, Yoshida and Eguchi (2007) to obtain an improved estimator. If we use the normal density to compute the importance weights, the resulting estimator takes the form of the one-step exponential tilting estimator. The proposed exponential tilting estimator is shown to be asymptotically equivalent to the regression estimator, but it avoids extreme weights and has some computational advantages over the empirical likelihood estimator. Variance estimation is also discussed and results from a limited simulation study are presented.
Release date: 2010-12-21 - 3. Comparison of survey regression techniques in the context of small area estimation of poverty ArchivedArticles and reports: 12-001-X201000211378Description:
One key to poverty alleviation or eradication in the third world is reliable information on the poor and their location, so that interventions and assistance can be effectively targeted to the neediest people. Small area estimation is one statistical technique that is used to monitor poverty and to decide on aid allocation in pursuit of the Millennium Development Goals. Elbers, Lanjouw and Lanjouw (ELL) (2003) proposed a small area estimation methodology for income-based or expenditure-based poverty measures, which is implemented by the World Bank in its poverty mapping projects via the involvement of the central statistical agencies in many third world countries, including Cambodia, Lao PDR, the Philippines, Thailand and Vietnam, and is incorporated into the World Bank software program PovMap. In this paper, the ELL methodology which consists of first modeling survey data and then applying that model to census information is presented and discussed with strong emphasis on the first phase, i.e., the fitting of regression models and on the estimated standard errors at the second phase. Other regression model fitting procedures such as the General Survey Regression (GSR) (as described in Lohr (1999) Chapter 11) and those used in existing small area estimation techniques: Pseudo-Empirical Best Linear Unbiased Prediction (Pseudo-EBLUP) approach (You and Rao 2002) and Iterative Weighted Estimating Equation (IWEE) method (You, Rao and Kovacevic 2003) are presented and compared with the ELL modeling strategy. The most significant difference between the ELL method and the other techniques is in the theoretical underpinning of the ELL model fitting procedure. An example based on the Philippines Family Income and Expenditure Survey is presented to show the differences in both the parameter estimates and their corresponding standard errors, and in the variance components generated from the different methods and the discussion is extended to the effect of these on the estimated accuracy of the final small area estimates themselves. The need for sound estimation of variance components, as well as regression estimates and estimates of their standard errors for small area estimation of poverty is emphasized.
Release date: 2010-12-21 - 4. Small area estimation of the number of firms' recruits by using multivariate models for count data ArchivedArticles and reports: 12-001-X201000211379Description:
The number of people recruited by firms in Local Labour Market Areas provides an important indicator of the reorganisation of the local productive processes. In Italy, this parameter can be estimated using the information collected in the Excelsior survey, although it does not provide reliable estimates for the domains of interest. In this paper we propose a multivariate small area estimation approach for count data based on the Multivariate Poisson-Log Normal distribution. This approach will be used to estimate the number of firm recruits both replacing departing employees and filling new positions. In the small area estimation framework, it is customary to assume that sampling variances and covariances are known. However, both they and the direct point estimates suffer from instability. Due to the rare nature of the phenomenon we are analysing, counts in some domains are equal to zero, and this produces estimates of sampling error covariances equal to zero. To account for the extra variability due to the estimated sampling covariance matrix, and to deal with the problem of unreasonable estimated variances and covariances in some domains, we propose an "integrated" approach where we jointly model the parameters of interest and the sampling error covariance matrices. We suggest a solution based again on the Poisson-Log Normal distribution to smooth variances and covariances. The results we obtain are encouraging: the proposed small area estimation model shows a better fit when compared to the Multivariate Normal-Normal (MNN) small area model, and it allows for a non-negligible increase in efficiency.
Release date: 2010-12-21 - 5. Linearization variance estimation for generalized raking estimators in the presence of nonresponse ArchivedArticles and reports: 12-001-X201000211380Description:
Alternative forms of linearization variance estimators for generalized raking estimators are defined via different choices of the weights applied (a) to residuals and (b) to the estimated regression coefficients used in calculating the residuals. Some theory is presented for three forms of generalized raking estimator, the classical raking ratio estimator, the 'maximum likelihood' raking estimator and the generalized regression estimator, and for associated linearization variance estimators. A simulation study is undertaken, based upon a labour force survey and an income and expenditure survey. Properties of the estimators are assessed with respect to both sampling and nonresponse. The study displays little difference between the properties of the alternative raking estimators for a given sampling scheme and nonresponse model. Amongst the variance estimators, the approach which weights residuals by the design weight can be severely biased in the presence of nonresponse. The approach which weights residuals by the calibrated weight tends to display much less bias. Varying the choice of the weights used to construct the regression coefficients has little impact.
Release date: 2010-12-21 - Articles and reports: 12-001-X201000211381Description:
Taylor linearization methods are often used to obtain variance estimators for calibration estimators of totals and nonlinear finite population (or census) parameters, such as ratios, regression and correlation coefficients, which can be expressed as smooth functions of totals. Taylor linearization is generally applicable to any sampling design, but it can lead to multiple variance estimators that are asymptotically design unbiased under repeated sampling. The choice among the variance estimators requires other considerations such as (i) approximate unbiasedness for the model variance of the estimator under an assumed model, and (ii) validity under a conditional repeated sampling framework. Demnati and Rao (2004) proposed a unified approach to deriving Taylor linearization variance estimators that leads directly to a unique variance estimator that satisfies the above considerations for general designs. When analyzing survey data, finite populations are often assumed to be generated from super-population models, and analytical inferences on model parameters are of interest. If the sampling fractions are small, then the sampling variance captures almost the entire variation generated by the design and model random processes. However, when the sampling fractions are not negligible, the model variance should be taken into account in order to construct valid inferences on model parameters under the combined process of generating the finite population from the assumed super-population model and the selection of the sample according to the specified sampling design. In this paper, we obtain an estimator of the total variance, using the Demnati-Rao approach, when the characteristics of interest are assumed to be random variables generated from a super-population model. We illustrate the method using ratio estimators and estimators defined as solutions to calibration weighted estimating equations. Simulation results on the performance of the proposed variance estimator for model parameters are also presented.
Release date: 2010-12-21 - 7. Statistical foundations of cell-phone surveys ArchivedArticles and reports: 12-001-X201000211382Description:
The size of the cell-phone-only population in the USA has increased rapidly in recent years and, correspondingly, researchers have begun to experiment with sampling and interviewing of cell-phone subscribers. We discuss statistical issues involved in the sampling design and estimation phases of cell-phone studies. This work is presented primarily in the context of a nonoverlapping dual-frame survey in which one frame and sample are employed for the landline population and a second frame and sample are employed for the cell-phone-only population. Additional considerations necessary for overlapping dual-frame surveys (where the cell-phone frame and sample include some of the landline population) are also discussed. We illustrate the methods using the design of the National Immunization Survey (NIS), which monitors the vaccination rates of children age 19-35 months and teens age 13-17 years. The NIS is a nationwide telephone survey, followed by a provider record check, conducted by the Centers for Disease Control and Prevention.
Release date: 2010-12-21 - Articles and reports: 12-001-X201000111244Description:
This paper considers the problem of selecting nonparametric models for small area estimation, which recently have received much attention. We develop a procedure based on the idea of fence method (Jiang, Rao, Gu and Nguyen 2008) for selecting the mean function for the small areas from a class of approximating splines. Simulation results show impressive performance of the new procedure even when the number of small areas is fairly small. The method is applied to a hospital graft failure dataset for selecting a nonparametric Fay-Herriot type model.
Release date: 2010-06-29 - Articles and reports: 12-001-X201000111246Description:
Many surveys employ weight adjustment procedures to reduce nonresponse bias. These adjustments make use of available auxiliary data. This paper addresses the issue of jackknife variance estimation for estimators that have been adjusted for nonresponse. Using the reverse approach for variance estimation proposed by Fay (1991) and Shao and Steel (1999), we study the effect of not re-calculating the nonresponse weight adjustment within each jackknife replicate. We show that the resulting 'shortcut' jackknife variance estimator tends to overestimate the true variance of point estimators in the case of several weight adjustment procedures used in practice. These theoretical results are confirmed through a simulation study where we compare the shortcut jackknife variance estimator with the full jackknife variance estimator obtained by re-calculating the nonresponse weight adjustment within each jackknife replicate.
Release date: 2010-06-29 - Articles and reports: 12-001-X201000111247Description:
In this paper, the problem of estimating the variance of various estimators of the population mean in two-phase sampling has been considered by jackknifing the two-phase calibrated weights of Hidiroglou and Särndal (1995, 1998). Several estimators of population mean available in the literature are shown to be the special cases of the technique developed here, including those suggested by Rao and Sitter (1995) and Sitter (1997). By following Raj (1965) and Srivenkataramana and Tracy (1989), some new estimators of the population mean are introduced and their variances are estimated through the proposed jackknife procedure. The variance of the chain ratio and regression type estimators due to Chand (1975) are also estimated using the jackknife. A simulation study is conducted to assess the efficiency of the proposed jackknife estimators relative to the usual estimators of variance.
Release date: 2010-06-29
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Articles and reports (13)
Articles and reports (13) (0 to 10 of 13 results)
- Articles and reports: 12-001-X201000211376Description:
This article develops computational tools, called indicators, for judging the effectiveness of the auxiliary information used to control nonresponse bias in survey estimates, obtained in this article by calibration. This work is motivated by the survey environment in a number of countries, notably in northern Europe, where many potential auxiliary variables are derived from reliable administrative registers for household and individuals. Many auxiliary vectors can be composed. There is a need to compare these vectors to assess their potential for reducing bias. The indicators in this article are designed to meet that need. They are used in surveys at Statistics Sweden. General survey conditions are considered: There is probability sampling from the finite population, by an arbitrary sampling design; nonresponse occurs. The probability of inclusion in the sample is known for each population unit; the probability of response is unknown, causing bias. The study variable (the y-variable) is observed for the set of respondents only. No matter what auxiliary vector is used in a calibration estimator (or in any other estimation method), a residual bias will always remain. The choice of a "best possible" auxiliary vector is guided by the indicators proposed in the article. Their background and computational features are described in the early sections of the article. Their theoretical background is explained. The concluding sections are devoted to empirical studies. One of these illustrates the selection of auxiliary variables in a survey at Statistics Sweden. A second empirical illustration is a simulation with a constructed finite population; a number of potential auxiliary vectors are ranked in order of preference with the aid of the indicators.
Release date: 2010-12-21 - Articles and reports: 12-001-X201000211377Description:
We consider the problem of parameter estimation with auxiliary information, where the auxiliary information takes the form of known moments. Calibration estimation is a typical example of using the moment conditions in sample surveys. Given the parametric form of the original distribution of the sample observations, we use the estimated importance sampling of Henmi, Yoshida and Eguchi (2007) to obtain an improved estimator. If we use the normal density to compute the importance weights, the resulting estimator takes the form of the one-step exponential tilting estimator. The proposed exponential tilting estimator is shown to be asymptotically equivalent to the regression estimator, but it avoids extreme weights and has some computational advantages over the empirical likelihood estimator. Variance estimation is also discussed and results from a limited simulation study are presented.
Release date: 2010-12-21 - 3. Comparison of survey regression techniques in the context of small area estimation of poverty ArchivedArticles and reports: 12-001-X201000211378Description:
One key to poverty alleviation or eradication in the third world is reliable information on the poor and their location, so that interventions and assistance can be effectively targeted to the neediest people. Small area estimation is one statistical technique that is used to monitor poverty and to decide on aid allocation in pursuit of the Millennium Development Goals. Elbers, Lanjouw and Lanjouw (ELL) (2003) proposed a small area estimation methodology for income-based or expenditure-based poverty measures, which is implemented by the World Bank in its poverty mapping projects via the involvement of the central statistical agencies in many third world countries, including Cambodia, Lao PDR, the Philippines, Thailand and Vietnam, and is incorporated into the World Bank software program PovMap. In this paper, the ELL methodology which consists of first modeling survey data and then applying that model to census information is presented and discussed with strong emphasis on the first phase, i.e., the fitting of regression models and on the estimated standard errors at the second phase. Other regression model fitting procedures such as the General Survey Regression (GSR) (as described in Lohr (1999) Chapter 11) and those used in existing small area estimation techniques: Pseudo-Empirical Best Linear Unbiased Prediction (Pseudo-EBLUP) approach (You and Rao 2002) and Iterative Weighted Estimating Equation (IWEE) method (You, Rao and Kovacevic 2003) are presented and compared with the ELL modeling strategy. The most significant difference between the ELL method and the other techniques is in the theoretical underpinning of the ELL model fitting procedure. An example based on the Philippines Family Income and Expenditure Survey is presented to show the differences in both the parameter estimates and their corresponding standard errors, and in the variance components generated from the different methods and the discussion is extended to the effect of these on the estimated accuracy of the final small area estimates themselves. The need for sound estimation of variance components, as well as regression estimates and estimates of their standard errors for small area estimation of poverty is emphasized.
Release date: 2010-12-21 - 4. Small area estimation of the number of firms' recruits by using multivariate models for count data ArchivedArticles and reports: 12-001-X201000211379Description:
The number of people recruited by firms in Local Labour Market Areas provides an important indicator of the reorganisation of the local productive processes. In Italy, this parameter can be estimated using the information collected in the Excelsior survey, although it does not provide reliable estimates for the domains of interest. In this paper we propose a multivariate small area estimation approach for count data based on the Multivariate Poisson-Log Normal distribution. This approach will be used to estimate the number of firm recruits both replacing departing employees and filling new positions. In the small area estimation framework, it is customary to assume that sampling variances and covariances are known. However, both they and the direct point estimates suffer from instability. Due to the rare nature of the phenomenon we are analysing, counts in some domains are equal to zero, and this produces estimates of sampling error covariances equal to zero. To account for the extra variability due to the estimated sampling covariance matrix, and to deal with the problem of unreasonable estimated variances and covariances in some domains, we propose an "integrated" approach where we jointly model the parameters of interest and the sampling error covariance matrices. We suggest a solution based again on the Poisson-Log Normal distribution to smooth variances and covariances. The results we obtain are encouraging: the proposed small area estimation model shows a better fit when compared to the Multivariate Normal-Normal (MNN) small area model, and it allows for a non-negligible increase in efficiency.
Release date: 2010-12-21 - 5. Linearization variance estimation for generalized raking estimators in the presence of nonresponse ArchivedArticles and reports: 12-001-X201000211380Description:
Alternative forms of linearization variance estimators for generalized raking estimators are defined via different choices of the weights applied (a) to residuals and (b) to the estimated regression coefficients used in calculating the residuals. Some theory is presented for three forms of generalized raking estimator, the classical raking ratio estimator, the 'maximum likelihood' raking estimator and the generalized regression estimator, and for associated linearization variance estimators. A simulation study is undertaken, based upon a labour force survey and an income and expenditure survey. Properties of the estimators are assessed with respect to both sampling and nonresponse. The study displays little difference between the properties of the alternative raking estimators for a given sampling scheme and nonresponse model. Amongst the variance estimators, the approach which weights residuals by the design weight can be severely biased in the presence of nonresponse. The approach which weights residuals by the calibrated weight tends to display much less bias. Varying the choice of the weights used to construct the regression coefficients has little impact.
Release date: 2010-12-21 - Articles and reports: 12-001-X201000211381Description:
Taylor linearization methods are often used to obtain variance estimators for calibration estimators of totals and nonlinear finite population (or census) parameters, such as ratios, regression and correlation coefficients, which can be expressed as smooth functions of totals. Taylor linearization is generally applicable to any sampling design, but it can lead to multiple variance estimators that are asymptotically design unbiased under repeated sampling. The choice among the variance estimators requires other considerations such as (i) approximate unbiasedness for the model variance of the estimator under an assumed model, and (ii) validity under a conditional repeated sampling framework. Demnati and Rao (2004) proposed a unified approach to deriving Taylor linearization variance estimators that leads directly to a unique variance estimator that satisfies the above considerations for general designs. When analyzing survey data, finite populations are often assumed to be generated from super-population models, and analytical inferences on model parameters are of interest. If the sampling fractions are small, then the sampling variance captures almost the entire variation generated by the design and model random processes. However, when the sampling fractions are not negligible, the model variance should be taken into account in order to construct valid inferences on model parameters under the combined process of generating the finite population from the assumed super-population model and the selection of the sample according to the specified sampling design. In this paper, we obtain an estimator of the total variance, using the Demnati-Rao approach, when the characteristics of interest are assumed to be random variables generated from a super-population model. We illustrate the method using ratio estimators and estimators defined as solutions to calibration weighted estimating equations. Simulation results on the performance of the proposed variance estimator for model parameters are also presented.
Release date: 2010-12-21 - 7. Statistical foundations of cell-phone surveys ArchivedArticles and reports: 12-001-X201000211382Description:
The size of the cell-phone-only population in the USA has increased rapidly in recent years and, correspondingly, researchers have begun to experiment with sampling and interviewing of cell-phone subscribers. We discuss statistical issues involved in the sampling design and estimation phases of cell-phone studies. This work is presented primarily in the context of a nonoverlapping dual-frame survey in which one frame and sample are employed for the landline population and a second frame and sample are employed for the cell-phone-only population. Additional considerations necessary for overlapping dual-frame surveys (where the cell-phone frame and sample include some of the landline population) are also discussed. We illustrate the methods using the design of the National Immunization Survey (NIS), which monitors the vaccination rates of children age 19-35 months and teens age 13-17 years. The NIS is a nationwide telephone survey, followed by a provider record check, conducted by the Centers for Disease Control and Prevention.
Release date: 2010-12-21 - Articles and reports: 12-001-X201000111244Description:
This paper considers the problem of selecting nonparametric models for small area estimation, which recently have received much attention. We develop a procedure based on the idea of fence method (Jiang, Rao, Gu and Nguyen 2008) for selecting the mean function for the small areas from a class of approximating splines. Simulation results show impressive performance of the new procedure even when the number of small areas is fairly small. The method is applied to a hospital graft failure dataset for selecting a nonparametric Fay-Herriot type model.
Release date: 2010-06-29 - Articles and reports: 12-001-X201000111246Description:
Many surveys employ weight adjustment procedures to reduce nonresponse bias. These adjustments make use of available auxiliary data. This paper addresses the issue of jackknife variance estimation for estimators that have been adjusted for nonresponse. Using the reverse approach for variance estimation proposed by Fay (1991) and Shao and Steel (1999), we study the effect of not re-calculating the nonresponse weight adjustment within each jackknife replicate. We show that the resulting 'shortcut' jackknife variance estimator tends to overestimate the true variance of point estimators in the case of several weight adjustment procedures used in practice. These theoretical results are confirmed through a simulation study where we compare the shortcut jackknife variance estimator with the full jackknife variance estimator obtained by re-calculating the nonresponse weight adjustment within each jackknife replicate.
Release date: 2010-06-29 - Articles and reports: 12-001-X201000111247Description:
In this paper, the problem of estimating the variance of various estimators of the population mean in two-phase sampling has been considered by jackknifing the two-phase calibrated weights of Hidiroglou and Särndal (1995, 1998). Several estimators of population mean available in the literature are shown to be the special cases of the technique developed here, including those suggested by Rao and Sitter (1995) and Sitter (1997). By following Raj (1965) and Srivenkataramana and Tracy (1989), some new estimators of the population mean are introduced and their variances are estimated through the proposed jackknife procedure. The variance of the chain ratio and regression type estimators due to Chand (1975) are also estimated using the jackknife. A simulation study is conducted to assess the efficiency of the proposed jackknife estimators relative to the usual estimators of variance.
Release date: 2010-06-29
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