Weighting and estimation
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All (14) (0 to 10 of 14 results)
- Articles and reports: 12-001-X202100100005Description:
Bayesian pooling strategies are used to solve precision problems related to statistical analyses of data from small areas. In such cases, the subpopulation samples are usually small, even though the population might not be. As an alternative, similar data can be pooled in order to reduce the number of parameters in the model. Many surveys consist of categorical data on each area, collected into a contingency table. We consider hierarchical Bayesian pooling models with a Dirichlet process prior for analyzing categorical data based on small areas. However, the prior used to pool such data frequently results in an overshrinkage problem. To mitigate for this problem, the parameters are separated into global and local effects. This study focuses on data pooling using a Dirichlet process prior. We compare the pooling models using bone mineral density (BMD) data taken from the Third National Health and Nutrition Examination Survey for the period 1988 to 1994 in the United States. Our analyses of the BMD data are performed using a Gibbs sampler and slice sampling to carry out the posterior computations.
Release date: 2021-06-24 - Articles and reports: 12-001-X201900200003Description:
Merging available sources of information is becoming increasingly important for improving estimates of population characteristics in a variety of fields. In presence of several independent probability samples from a finite population we investigate options for a combined estimator of the population total, based on either a linear combination of the separate estimators or on the combined sample approach. A linear combination estimator based on estimated variances can be biased as the separate estimators of the population total can be highly correlated to their respective variance estimators. We illustrate the possibility to use the combined sample to estimate the variances of the separate estimators, which results in general pooled variance estimators. These pooled variance estimators use all available information and have potential to significantly reduce bias of a linear combination of separate estimators.
Release date: 2019-06-27 - Articles and reports: 12-001-X201800254952Description:
Panel surveys are frequently used to measure the evolution of parameters over time. Panel samples may suffer from different types of unit non-response, which is currently handled by estimating the response probabilities and by reweighting respondents. In this work, we consider estimation and variance estimation under unit non-response for panel surveys. Extending the work by Kim and Kim (2007) for several times, we consider a propensity score adjusted estimator accounting for initial non-response and attrition, and propose a suitable variance estimator. It is then extended to cover most estimators encountered in surveys, including calibrated estimators, complex parameters and longitudinal estimators. The properties of the proposed variance estimator and of a simplified variance estimator are estimated through a simulation study. An illustration of the proposed methods on data from the ELFE survey is also presented.
Release date: 2018-12-20 - 4. Observed best prediction via nested-error regression with potentially misspecified mean and variance ArchivedArticles and reports: 12-001-X201500114200Description:
We consider the observed best prediction (OBP; Jiang, Nguyen and Rao 2011) for small area estimation under the nested-error regression model, where both the mean and variance functions may be misspecified. We show via a simulation study that the OBP may significantly outperform the empirical best linear unbiased prediction (EBLUP) method not just in the overall mean squared prediction error (MSPE) but also in the area-specific MSPE for every one of the small areas. A bootstrap method is proposed for estimating the design-based area-specific MSPE, which is simple and always produces positive MSPE estimates. The performance of the proposed MSPE estimator is evaluated through a simulation study. An application to the Television School and Family Smoking Prevention and Cessation study is considered.
Release date: 2015-06-29 - Articles and reports: 11-522-X201300014286Description:
The Étude Longitudinale Française depuis l’Enfance (ELFE) [French longitudinal study from childhood on], which began in 2011, involves over 18,300 infants whose parents agreed to participate when they were in the maternity hospital. This cohort survey, which will track the children from birth to adulthood, covers the many aspects of their lives from the perspective of social science, health and environmental health. In randomly selected maternity hospitals, all infants in the target population, who were born on one of 25 days distributed across the four seasons, were chosen. This sample is the outcome of a non-standard sampling scheme that we call product sampling. In this survey, it takes the form of the cross-tabulation between two independent samples: a sampling of maternity hospitals and a sampling of days. While it is easy to imagine a cluster effect due to the sampling of maternity hospitals, one can also imagine a cluster effect due to the sampling of days. The scheme’s time dimension therefore cannot be ignored if the desired estimates are subject to daily or seasonal variation. While this non-standard scheme can be viewed as a particular kind of two-phase design, it needs to be defined within a more specific framework. Following a comparison of the product scheme with a conventional two-stage design, we propose variance estimators specially formulated for this sampling scheme. Our ideas are illustrated with a simulation study.
Release date: 2014-10-31 - Articles and reports: 12-001-X201300211888Description:
When the study variables are functional and storage capacities are limited or transmission costs are high, using survey techniques to select a portion of the observations of the population is an interesting alternative to using signal compression techniques. In this context of functional data, our focus in this study is on estimating the mean electricity consumption curve over a one-week period. We compare different estimation strategies that take account of a piece of auxiliary information such as the mean consumption for the previous period. The first strategy consists in using a simple random sampling design without replacement, then incorporating the auxiliary information into the estimator by introducing a functional linear model. The second approach consists in incorporating the auxiliary information into the sampling designs by considering unequal probability designs, such as stratified and pi designs. We then address the issue of constructing confidence bands for these estimators of the mean. When effective estimators of the covariance function are available and the mean estimator satisfies a functional central limit theorem, it is possible to use a fast technique for constructing confidence bands, based on the simulation of Gaussian processes. This approach is compared with bootstrap techniques that have been adapted to take account of the functional nature of the data.
Release date: 2014-01-15 - 7. 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 - 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-X200900211045Description:
In analysis of sample survey data, degrees-of-freedom quantities are often used to assess the stability of design-based variance estimators. For example, these degrees-of-freedom values are used in construction of confidence intervals based on t distribution approximations; and of related t tests. In addition, a small degrees-of-freedom term provides a qualitative indication of the possible limitations of a given variance estimator in a specific application. Degrees-of-freedom calculations sometimes are based on forms of the Satterthwaite approximation. These Satterthwaite-based calculations depend primarily on the relative magnitudes of stratum-level variances. However, for designs involving a small number of primary units selected per stratum, standard stratum-level variance estimators provide limited information on the true stratum variances. For such cases, customary Satterthwaite-based calculations can be problematic, especially in analyses for subpopulations that are concentrated in a relatively small number of strata. To address this problem, this paper uses estimated within-primary-sample-unit (within PSU) variances to provide auxiliary information regarding the relative magnitudes of the overall stratum-level variances. Analytic results indicate that the resulting degrees-of-freedom estimator will be better than modified Satterthwaite-type estimators provided: (a) the overall stratum-level variances are approximately proportional to the corresponding within-stratum variances; and (b) the variances of the within-PSU variance estimators are relatively small. In addition, this paper develops errors-in-variables methods that can be used to check conditions (a) and (b) empirically. For these model checks, we develop simulation-based reference distributions, which differ substantially from reference distributions based on customary large-sample normal approximations. The proposed methods are applied to four variables from the U.S. Third National Health and Nutrition Examination Survey (NHANES III).
Release date: 2009-12-23 - Articles and reports: 12-001-X20070019850Description:
Auxiliary information is often used to improve the precision of survey estimators of finite population means and totals through ratio or linear regression estimation techniques. Resulting estimators have good theoretical and practical properties, including invariance, calibration and design consistency. However, it is not always clear that ratio or linear models are good approximations to the true relationship between the auxiliary variables and the variable of interest in the survey, resulting in efficiency loss when the model is not appropriate. In this article, we explain how regression estimation can be extended to incorporate semiparametric regression models, in both simple and more complicated designs. While maintaining the good theoretical and practical properties of the linear models, semiparametric models are better able to capture complicated relationships between variables. This often results in substantial gains in efficiency. The applicability of the approach for complex designs using multiple types of auxiliary variables will be illustrated by estimating several acidification-related characteristics for a survey of lakes in the Northeastern US.
Release date: 2007-06-28
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Analysis (14)
Analysis (14) (0 to 10 of 14 results)
- Articles and reports: 12-001-X202100100005Description:
Bayesian pooling strategies are used to solve precision problems related to statistical analyses of data from small areas. In such cases, the subpopulation samples are usually small, even though the population might not be. As an alternative, similar data can be pooled in order to reduce the number of parameters in the model. Many surveys consist of categorical data on each area, collected into a contingency table. We consider hierarchical Bayesian pooling models with a Dirichlet process prior for analyzing categorical data based on small areas. However, the prior used to pool such data frequently results in an overshrinkage problem. To mitigate for this problem, the parameters are separated into global and local effects. This study focuses on data pooling using a Dirichlet process prior. We compare the pooling models using bone mineral density (BMD) data taken from the Third National Health and Nutrition Examination Survey for the period 1988 to 1994 in the United States. Our analyses of the BMD data are performed using a Gibbs sampler and slice sampling to carry out the posterior computations.
Release date: 2021-06-24 - Articles and reports: 12-001-X201900200003Description:
Merging available sources of information is becoming increasingly important for improving estimates of population characteristics in a variety of fields. In presence of several independent probability samples from a finite population we investigate options for a combined estimator of the population total, based on either a linear combination of the separate estimators or on the combined sample approach. A linear combination estimator based on estimated variances can be biased as the separate estimators of the population total can be highly correlated to their respective variance estimators. We illustrate the possibility to use the combined sample to estimate the variances of the separate estimators, which results in general pooled variance estimators. These pooled variance estimators use all available information and have potential to significantly reduce bias of a linear combination of separate estimators.
Release date: 2019-06-27 - Articles and reports: 12-001-X201800254952Description:
Panel surveys are frequently used to measure the evolution of parameters over time. Panel samples may suffer from different types of unit non-response, which is currently handled by estimating the response probabilities and by reweighting respondents. In this work, we consider estimation and variance estimation under unit non-response for panel surveys. Extending the work by Kim and Kim (2007) for several times, we consider a propensity score adjusted estimator accounting for initial non-response and attrition, and propose a suitable variance estimator. It is then extended to cover most estimators encountered in surveys, including calibrated estimators, complex parameters and longitudinal estimators. The properties of the proposed variance estimator and of a simplified variance estimator are estimated through a simulation study. An illustration of the proposed methods on data from the ELFE survey is also presented.
Release date: 2018-12-20 - 4. Observed best prediction via nested-error regression with potentially misspecified mean and variance ArchivedArticles and reports: 12-001-X201500114200Description:
We consider the observed best prediction (OBP; Jiang, Nguyen and Rao 2011) for small area estimation under the nested-error regression model, where both the mean and variance functions may be misspecified. We show via a simulation study that the OBP may significantly outperform the empirical best linear unbiased prediction (EBLUP) method not just in the overall mean squared prediction error (MSPE) but also in the area-specific MSPE for every one of the small areas. A bootstrap method is proposed for estimating the design-based area-specific MSPE, which is simple and always produces positive MSPE estimates. The performance of the proposed MSPE estimator is evaluated through a simulation study. An application to the Television School and Family Smoking Prevention and Cessation study is considered.
Release date: 2015-06-29 - Articles and reports: 11-522-X201300014286Description:
The Étude Longitudinale Française depuis l’Enfance (ELFE) [French longitudinal study from childhood on], which began in 2011, involves over 18,300 infants whose parents agreed to participate when they were in the maternity hospital. This cohort survey, which will track the children from birth to adulthood, covers the many aspects of their lives from the perspective of social science, health and environmental health. In randomly selected maternity hospitals, all infants in the target population, who were born on one of 25 days distributed across the four seasons, were chosen. This sample is the outcome of a non-standard sampling scheme that we call product sampling. In this survey, it takes the form of the cross-tabulation between two independent samples: a sampling of maternity hospitals and a sampling of days. While it is easy to imagine a cluster effect due to the sampling of maternity hospitals, one can also imagine a cluster effect due to the sampling of days. The scheme’s time dimension therefore cannot be ignored if the desired estimates are subject to daily or seasonal variation. While this non-standard scheme can be viewed as a particular kind of two-phase design, it needs to be defined within a more specific framework. Following a comparison of the product scheme with a conventional two-stage design, we propose variance estimators specially formulated for this sampling scheme. Our ideas are illustrated with a simulation study.
Release date: 2014-10-31 - Articles and reports: 12-001-X201300211888Description:
When the study variables are functional and storage capacities are limited or transmission costs are high, using survey techniques to select a portion of the observations of the population is an interesting alternative to using signal compression techniques. In this context of functional data, our focus in this study is on estimating the mean electricity consumption curve over a one-week period. We compare different estimation strategies that take account of a piece of auxiliary information such as the mean consumption for the previous period. The first strategy consists in using a simple random sampling design without replacement, then incorporating the auxiliary information into the estimator by introducing a functional linear model. The second approach consists in incorporating the auxiliary information into the sampling designs by considering unequal probability designs, such as stratified and pi designs. We then address the issue of constructing confidence bands for these estimators of the mean. When effective estimators of the covariance function are available and the mean estimator satisfies a functional central limit theorem, it is possible to use a fast technique for constructing confidence bands, based on the simulation of Gaussian processes. This approach is compared with bootstrap techniques that have been adapted to take account of the functional nature of the data.
Release date: 2014-01-15 - 7. 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 - 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-X200900211045Description:
In analysis of sample survey data, degrees-of-freedom quantities are often used to assess the stability of design-based variance estimators. For example, these degrees-of-freedom values are used in construction of confidence intervals based on t distribution approximations; and of related t tests. In addition, a small degrees-of-freedom term provides a qualitative indication of the possible limitations of a given variance estimator in a specific application. Degrees-of-freedom calculations sometimes are based on forms of the Satterthwaite approximation. These Satterthwaite-based calculations depend primarily on the relative magnitudes of stratum-level variances. However, for designs involving a small number of primary units selected per stratum, standard stratum-level variance estimators provide limited information on the true stratum variances. For such cases, customary Satterthwaite-based calculations can be problematic, especially in analyses for subpopulations that are concentrated in a relatively small number of strata. To address this problem, this paper uses estimated within-primary-sample-unit (within PSU) variances to provide auxiliary information regarding the relative magnitudes of the overall stratum-level variances. Analytic results indicate that the resulting degrees-of-freedom estimator will be better than modified Satterthwaite-type estimators provided: (a) the overall stratum-level variances are approximately proportional to the corresponding within-stratum variances; and (b) the variances of the within-PSU variance estimators are relatively small. In addition, this paper develops errors-in-variables methods that can be used to check conditions (a) and (b) empirically. For these model checks, we develop simulation-based reference distributions, which differ substantially from reference distributions based on customary large-sample normal approximations. The proposed methods are applied to four variables from the U.S. Third National Health and Nutrition Examination Survey (NHANES III).
Release date: 2009-12-23 - Articles and reports: 12-001-X20070019850Description:
Auxiliary information is often used to improve the precision of survey estimators of finite population means and totals through ratio or linear regression estimation techniques. Resulting estimators have good theoretical and practical properties, including invariance, calibration and design consistency. However, it is not always clear that ratio or linear models are good approximations to the true relationship between the auxiliary variables and the variable of interest in the survey, resulting in efficiency loss when the model is not appropriate. In this article, we explain how regression estimation can be extended to incorporate semiparametric regression models, in both simple and more complicated designs. While maintaining the good theoretical and practical properties of the linear models, semiparametric models are better able to capture complicated relationships between variables. This often results in substantial gains in efficiency. The applicability of the approach for complex designs using multiple types of auxiliary variables will be illustrated by estimating several acidification-related characteristics for a survey of lakes in the Northeastern US.
Release date: 2007-06-28
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