Weighting and estimation

Filter results by

Search Help
Currently selected filters that can be removed

Keyword(s)

Type

1 facets displayed. 0 facets selected.

Geography

1 facets displayed. 0 facets selected.

Content

1 facets displayed. 0 facets selected.
Sort Help
entries

Results

All (24)

All (24) (0 to 10 of 24 results)

  • Articles and reports: 11-522-X202200100005
    Description: Sampling variance smoothing is an important topic in small area estimation. In this paper, we propose sampling variance smoothing methods for small area proportion estimation. In particular, we consider the generalized variance function and design effect methods for sampling variance smoothing. We evaluate and compare the smoothed sampling variances and small area estimates based on the smoothed variance estimates through analysis of survey data from Statistics Canada. The results from real data analysis indicate that the proposed sampling variance smoothing methods work very well for small area estimation.
    Release date: 2024-03-25

  • Articles and reports: 12-001-X202200100002
    Description:

    We consider an intercept only linear random effects model for analysis of data from a two stage cluster sampling design. At the first stage a simple random sample of clusters is drawn, and at the second stage a simple random sample of elementary units is taken within each selected cluster. The response variable is assumed to consist of a cluster-level random effect plus an independent error term with known variance. The objects of inference are the mean of the outcome variable and the random effect variance. With a more complex two stage sampling design, the use of an approach based on an estimated pairwise composite likelihood function has appealing properties. Our purpose is to use our simpler context to compare the results of likelihood inference with inference based on a pairwise composite likelihood function that is treated as an approximate likelihood, in particular treated as the likelihood component in Bayesian inference. In order to provide credible intervals having frequentist coverage close to nominal values, the pairwise composite likelihood function and corresponding posterior density need modification, such as a curvature adjustment. Through simulation studies, we investigate the performance of an adjustment proposed in the literature, and find that it works well for the mean but provides credible intervals for the random effect variance that suffer from under-coverage. We propose possible future directions including extensions to the case of a complex design.

    Release date: 2022-06-21

  • Articles and reports: 12-001-X202100200007
    Description:

    In this paper, we consider the Fay-Herriot model for small area estimation. In particular, we are interested in the impact of sampling variance smoothing and modeling on the model-based estimates. We present methods of smoothing and modeling for the sampling variances and apply the proposed models to a real data analysis. Our results indicate that sampling variance smoothing can improve the efficiency and accuracy of the model-based estimator. For sampling variance modeling, the HB models of You (2016) and Sugasawa, Tamae and Kubokawa (2017) perform equally well to improve the direct survey estimates.

    Release date: 2022-01-06

  • Articles and reports: 12-001-X201600114540
    Description:

    In this paper, we compare the EBLUP and pseudo-EBLUP estimators for small area estimation under the nested error regression model and three area level model-based estimators using the Fay-Herriot model. We conduct a design-based simulation study to compare the model-based estimators for unit level and area level models under informative and non-informative sampling. In particular, we are interested in the confidence interval coverage rate of the unit level and area level estimators. We also compare the estimators if the model has been misspecified. Our simulation results show that estimators based on the unit level model perform better than those based on the area level. The pseudo-EBLUP estimator is the best among unit level and area level estimators.

    Release date: 2016-06-22

  • Articles and reports: 12-001-X201300111830
    Description:

    We consider two different self-benchmarking methods for the estimation of small area means based on the Fay-Herriot (FH) area level model: the method of You and Rao (2002) applied to the FH model and the method of Wang, Fuller and Qu (2008) based on augmented models. We derive an estimator of the mean squared prediction error (MSPE) of the You-Rao (YR) estimator of a small area mean that, under the true model, is correct to second-order terms. We report the results of a simulation study on the relative bias of the MSPE estimator of the YR estimator and the MSPE estimator of the Wang, Fuller and Qu (WFQ) estimator obtained under an augmented model. We also study the MSPE and the estimators of MSPE for the YR and WFQ estimators obtained under a misspecified model.

    Release date: 2013-06-28

  • Articles and reports: 12-001-X201100111445
    Description:

    In this paper we study small area estimation using area level models. We first consider the Fay-Herriot model (Fay and Herriot 1979) for the case of smoothed known sampling variances and the You-Chapman model (You and Chapman 2006) for the case of sampling variance modeling. Then we consider hierarchical Bayes (HB) spatial models that extend the Fay-Herriot and You-Chapman models by capturing both the geographically unstructured heterogeneity and spatial correlation effects among areas for local smoothing. The proposed models are implemented using the Gibbs sampling method for fully Bayesian inference. We apply the proposed models to the analysis of health survey data and make comparisons among the HB model-based estimates and direct design-based estimates. Our results have shown that the HB model-based estimates perform much better than the direct estimates. In addition, the proposed area level spatial models achieve smaller CVs than the Fay-Herriot and You-Chapman models, particularly for the areas with three or more neighbouring areas. Bayesian model comparison and model fit analysis are also presented.

    Release date: 2011-06-29

  • Articles and reports: 12-001-X201100111448
    Description:

    In two-phase sampling for stratification, the second-phase sample is selected by a stratified sample based on the information observed in the first-phase sample. We develop a replication-based bias adjusted variance estimator that extends the method of Kim, Navarro and Fuller (2006). The proposed method is also applicable when the first-phase sampling rate is not negligible and when second-phase sample selection is unequal probability Poisson sampling within each stratum. The proposed method can be extended to variance estimation for two-phase regression estimators. Results from a limited simulation study are presented.

    Release date: 2011-06-29

  • Articles and reports: 12-001-X201000111246
    Description:

    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-X200800110614
    Geography: Canada
    Description:

    The Canadian Labour Force Survey (LFS) produces monthly estimates of the unemployment rate at national and provincial levels. The LFS also releases unemployment estimates for sub-provincial areas such as Census Metropolitan Areas (CMAs) and Urban Centers (UCs). However, for some sub-provincial areas, the direct estimates are not reliable since the sample size in some areas is quite small. The small area estimation in LFS concerns estimation of unemployment rates for local sub-provincial areas such as CMA/UCs using small area models. In this paper, we will discuss various models including the Fay-Herriot model and cross-sectional and time series models. In particular, an integrated non-linear mixed effects model will be proposed under the hierarchical Bayes (HB) framework for the LFS unemployment rate estimation. Monthly Employment Insurance (EI) beneficiary data at the CMA/UC level are used as auxiliary covariates in the model. A HB approach with the Gibbs sampling method is used to obtain the estimates of posterior means and posterior variances of the CMA/UC level unemployment rates. The proposed HB model leads to reliable model-based estimates in terms of CV reduction. Model fit analysis and comparison of the model-based estimates with the direct estimates are presented in the paper.

    Release date: 2008-06-26

  • Articles and reports: 12-001-X20060019263
    Description:

    In small area estimation, area level models such as the Fay - Herriot model (Fay and Herriot 1979) are widely used to obtain efficient model-based estimators for small areas. The sampling error variances are customarily assumed to be known in the model. In this paper we consider the situation where the sampling error variances are estimated individually by direct estimators. A full hierarchical Bayes (HB) model is constructed for the direct survey estimators and the sampling error variances estimators. The Gibbs sampling method is employed to obtain the small area HB estimators. The proposed HB approach automatically takes account of the extra uncertainty of estimating the sampling error variances, especially when the area-specific sample sizes are small. We compare the proposed HB model with the Fay - Herriot model through analysis of two survey data sets. Our results have shown that the proposed HB estimators perform quite well compared to the direct estimates. We also discussed the problem of priors on the variance components.

    Release date: 2006-07-20
Data (0)

Data (0) (0 results)

No content available at this time.

Analysis (24)

Analysis (24) (0 to 10 of 24 results)

  • Articles and reports: 11-522-X202200100005
    Description: Sampling variance smoothing is an important topic in small area estimation. In this paper, we propose sampling variance smoothing methods for small area proportion estimation. In particular, we consider the generalized variance function and design effect methods for sampling variance smoothing. We evaluate and compare the smoothed sampling variances and small area estimates based on the smoothed variance estimates through analysis of survey data from Statistics Canada. The results from real data analysis indicate that the proposed sampling variance smoothing methods work very well for small area estimation.
    Release date: 2024-03-25

  • Articles and reports: 12-001-X202200100002
    Description:

    We consider an intercept only linear random effects model for analysis of data from a two stage cluster sampling design. At the first stage a simple random sample of clusters is drawn, and at the second stage a simple random sample of elementary units is taken within each selected cluster. The response variable is assumed to consist of a cluster-level random effect plus an independent error term with known variance. The objects of inference are the mean of the outcome variable and the random effect variance. With a more complex two stage sampling design, the use of an approach based on an estimated pairwise composite likelihood function has appealing properties. Our purpose is to use our simpler context to compare the results of likelihood inference with inference based on a pairwise composite likelihood function that is treated as an approximate likelihood, in particular treated as the likelihood component in Bayesian inference. In order to provide credible intervals having frequentist coverage close to nominal values, the pairwise composite likelihood function and corresponding posterior density need modification, such as a curvature adjustment. Through simulation studies, we investigate the performance of an adjustment proposed in the literature, and find that it works well for the mean but provides credible intervals for the random effect variance that suffer from under-coverage. We propose possible future directions including extensions to the case of a complex design.

    Release date: 2022-06-21

  • Articles and reports: 12-001-X202100200007
    Description:

    In this paper, we consider the Fay-Herriot model for small area estimation. In particular, we are interested in the impact of sampling variance smoothing and modeling on the model-based estimates. We present methods of smoothing and modeling for the sampling variances and apply the proposed models to a real data analysis. Our results indicate that sampling variance smoothing can improve the efficiency and accuracy of the model-based estimator. For sampling variance modeling, the HB models of You (2016) and Sugasawa, Tamae and Kubokawa (2017) perform equally well to improve the direct survey estimates.

    Release date: 2022-01-06

  • Articles and reports: 12-001-X201600114540
    Description:

    In this paper, we compare the EBLUP and pseudo-EBLUP estimators for small area estimation under the nested error regression model and three area level model-based estimators using the Fay-Herriot model. We conduct a design-based simulation study to compare the model-based estimators for unit level and area level models under informative and non-informative sampling. In particular, we are interested in the confidence interval coverage rate of the unit level and area level estimators. We also compare the estimators if the model has been misspecified. Our simulation results show that estimators based on the unit level model perform better than those based on the area level. The pseudo-EBLUP estimator is the best among unit level and area level estimators.

    Release date: 2016-06-22

  • Articles and reports: 12-001-X201300111830
    Description:

    We consider two different self-benchmarking methods for the estimation of small area means based on the Fay-Herriot (FH) area level model: the method of You and Rao (2002) applied to the FH model and the method of Wang, Fuller and Qu (2008) based on augmented models. We derive an estimator of the mean squared prediction error (MSPE) of the You-Rao (YR) estimator of a small area mean that, under the true model, is correct to second-order terms. We report the results of a simulation study on the relative bias of the MSPE estimator of the YR estimator and the MSPE estimator of the Wang, Fuller and Qu (WFQ) estimator obtained under an augmented model. We also study the MSPE and the estimators of MSPE for the YR and WFQ estimators obtained under a misspecified model.

    Release date: 2013-06-28

  • Articles and reports: 12-001-X201100111445
    Description:

    In this paper we study small area estimation using area level models. We first consider the Fay-Herriot model (Fay and Herriot 1979) for the case of smoothed known sampling variances and the You-Chapman model (You and Chapman 2006) for the case of sampling variance modeling. Then we consider hierarchical Bayes (HB) spatial models that extend the Fay-Herriot and You-Chapman models by capturing both the geographically unstructured heterogeneity and spatial correlation effects among areas for local smoothing. The proposed models are implemented using the Gibbs sampling method for fully Bayesian inference. We apply the proposed models to the analysis of health survey data and make comparisons among the HB model-based estimates and direct design-based estimates. Our results have shown that the HB model-based estimates perform much better than the direct estimates. In addition, the proposed area level spatial models achieve smaller CVs than the Fay-Herriot and You-Chapman models, particularly for the areas with three or more neighbouring areas. Bayesian model comparison and model fit analysis are also presented.

    Release date: 2011-06-29

  • Articles and reports: 12-001-X201100111448
    Description:

    In two-phase sampling for stratification, the second-phase sample is selected by a stratified sample based on the information observed in the first-phase sample. We develop a replication-based bias adjusted variance estimator that extends the method of Kim, Navarro and Fuller (2006). The proposed method is also applicable when the first-phase sampling rate is not negligible and when second-phase sample selection is unequal probability Poisson sampling within each stratum. The proposed method can be extended to variance estimation for two-phase regression estimators. Results from a limited simulation study are presented.

    Release date: 2011-06-29

  • Articles and reports: 12-001-X201000111246
    Description:

    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-X200800110614
    Geography: Canada
    Description:

    The Canadian Labour Force Survey (LFS) produces monthly estimates of the unemployment rate at national and provincial levels. The LFS also releases unemployment estimates for sub-provincial areas such as Census Metropolitan Areas (CMAs) and Urban Centers (UCs). However, for some sub-provincial areas, the direct estimates are not reliable since the sample size in some areas is quite small. The small area estimation in LFS concerns estimation of unemployment rates for local sub-provincial areas such as CMA/UCs using small area models. In this paper, we will discuss various models including the Fay-Herriot model and cross-sectional and time series models. In particular, an integrated non-linear mixed effects model will be proposed under the hierarchical Bayes (HB) framework for the LFS unemployment rate estimation. Monthly Employment Insurance (EI) beneficiary data at the CMA/UC level are used as auxiliary covariates in the model. A HB approach with the Gibbs sampling method is used to obtain the estimates of posterior means and posterior variances of the CMA/UC level unemployment rates. The proposed HB model leads to reliable model-based estimates in terms of CV reduction. Model fit analysis and comparison of the model-based estimates with the direct estimates are presented in the paper.

    Release date: 2008-06-26

  • Articles and reports: 12-001-X20060019263
    Description:

    In small area estimation, area level models such as the Fay - Herriot model (Fay and Herriot 1979) are widely used to obtain efficient model-based estimators for small areas. The sampling error variances are customarily assumed to be known in the model. In this paper we consider the situation where the sampling error variances are estimated individually by direct estimators. A full hierarchical Bayes (HB) model is constructed for the direct survey estimators and the sampling error variances estimators. The Gibbs sampling method is employed to obtain the small area HB estimators. The proposed HB approach automatically takes account of the extra uncertainty of estimating the sampling error variances, especially when the area-specific sample sizes are small. We compare the proposed HB model with the Fay - Herriot model through analysis of two survey data sets. Our results have shown that the proposed HB estimators perform quite well compared to the direct estimates. We also discussed the problem of priors on the variance components.

    Release date: 2006-07-20
Reference (0)

Reference (0) (0 results)

No content available at this time.

Date modified: