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Mean squared error estimators of small area means using survey weights
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| Zeitschriftentitel: | Canadian Journal of Statistics |
|---|---|
| Personen und Körperschaften: | , |
| In: | Canadian Journal of Statistics, 38, 2010, 4, S. 598-608 |
| Format: | E-Article |
| Sprache: | Englisch |
| veröffentlicht: |
Wiley
|
| Schlagwörter: |
| author_facet |
Torabi, Mahmoud Rao, Jon N. K. Torabi, Mahmoud Rao, Jon N. K. |
|---|---|
| author |
Torabi, Mahmoud Rao, Jon N. K. |
| spellingShingle |
Torabi, Mahmoud Rao, Jon N. K. Canadian Journal of Statistics Mean squared error estimators of small area means using survey weights Statistics, Probability and Uncertainty Statistics and Probability |
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torabi, mahmoud |
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Torabi, Mahmoud Rao, Jon N. K. 0319-5724 1708-945X Wiley Statistics, Probability and Uncertainty Statistics and Probability http://dx.doi.org/10.1002/cjs.10078 <jats:title>Abstract</jats:title><jats:p>Using survey weights, You & Rao [You and Rao, The Canadian Journal of Statistics 2002; 30, 431–439] proposed a pseudo‐empirical best linear unbiased prediction (pseudo‐EBLUP) estimator of a small area mean under a nested error linear regression model. This estimator borrows strength across areas through a linking model, and makes use of survey weights to ensure design consistency and preserve benchmarking property in the sense that the estimators add up to a reliable direct estimator of the mean of a large area covering the small areas. In this article, a second‐order approximation to the mean squared error (MSE) of the pseudo‐EBLUP estimator of a small area mean is derived. Using this approximation, an estimator of MSE that is nearly unbiased is derived; the MSE estimator of You & Rao [You and Rao, The Canadian Journal of Statistics 2002; 30, 431–439] ignored cross‐product terms in the MSE and hence it is biased. Empirical results on the performance of the proposed MSE estimator are also presented. <jats:italic>The Canadian Journal of Statistics</jats:italic> 38: 598–608; 2010 © 2010 Statistical Society of Canada</jats:p> Mean squared error estimators of small area means using survey weights Canadian Journal of Statistics |
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Mean squared error estimators of small area means using survey weights |
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Mean squared error estimators of small area means using survey weights |
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Mean squared error estimators of small area means using survey weights |
| title_fullStr |
Mean squared error estimators of small area means using survey weights |
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Mean squared error estimators of small area means using survey weights |
| title_short |
Mean squared error estimators of small area means using survey weights |
| title_sort |
mean squared error estimators of small area means using survey weights |
| topic |
Statistics, Probability and Uncertainty Statistics and Probability |
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http://dx.doi.org/10.1002/cjs.10078 |
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2010 |
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598-608 |
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<jats:title>Abstract</jats:title><jats:p>Using survey weights, You & Rao [You and Rao, The Canadian Journal of Statistics 2002; 30, 431–439] proposed a pseudo‐empirical best linear unbiased prediction (pseudo‐EBLUP) estimator of a small area mean under a nested error linear regression model. This estimator borrows strength across areas through a linking model, and makes use of survey weights to ensure design consistency and preserve benchmarking property in the sense that the estimators add up to a reliable direct estimator of the mean of a large area covering the small areas. In this article, a second‐order approximation to the mean squared error (MSE) of the pseudo‐EBLUP estimator of a small area mean is derived. Using this approximation, an estimator of MSE that is nearly unbiased is derived; the MSE estimator of You & Rao [You and Rao, The Canadian Journal of Statistics 2002; 30, 431–439] ignored cross‐product terms in the MSE and hence it is biased. Empirical results on the performance of the proposed MSE estimator are also presented. <jats:italic>The Canadian Journal of Statistics</jats:italic> 38: 598–608; 2010 © 2010 Statistical Society of Canada</jats:p> |
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| author | Torabi, Mahmoud, Rao, Jon N. K. |
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| description | <jats:title>Abstract</jats:title><jats:p>Using survey weights, You & Rao [You and Rao, The Canadian Journal of Statistics 2002; 30, 431–439] proposed a pseudo‐empirical best linear unbiased prediction (pseudo‐EBLUP) estimator of a small area mean under a nested error linear regression model. This estimator borrows strength across areas through a linking model, and makes use of survey weights to ensure design consistency and preserve benchmarking property in the sense that the estimators add up to a reliable direct estimator of the mean of a large area covering the small areas. In this article, a second‐order approximation to the mean squared error (MSE) of the pseudo‐EBLUP estimator of a small area mean is derived. Using this approximation, an estimator of MSE that is nearly unbiased is derived; the MSE estimator of You & Rao [You and Rao, The Canadian Journal of Statistics 2002; 30, 431–439] ignored cross‐product terms in the MSE and hence it is biased. Empirical results on the performance of the proposed MSE estimator are also presented. <jats:italic>The Canadian Journal of Statistics</jats:italic> 38: 598–608; 2010 © 2010 Statistical Society of Canada</jats:p> |
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| spelling | Torabi, Mahmoud Rao, Jon N. K. 0319-5724 1708-945X Wiley Statistics, Probability and Uncertainty Statistics and Probability http://dx.doi.org/10.1002/cjs.10078 <jats:title>Abstract</jats:title><jats:p>Using survey weights, You & Rao [You and Rao, The Canadian Journal of Statistics 2002; 30, 431–439] proposed a pseudo‐empirical best linear unbiased prediction (pseudo‐EBLUP) estimator of a small area mean under a nested error linear regression model. This estimator borrows strength across areas through a linking model, and makes use of survey weights to ensure design consistency and preserve benchmarking property in the sense that the estimators add up to a reliable direct estimator of the mean of a large area covering the small areas. In this article, a second‐order approximation to the mean squared error (MSE) of the pseudo‐EBLUP estimator of a small area mean is derived. Using this approximation, an estimator of MSE that is nearly unbiased is derived; the MSE estimator of You & Rao [You and Rao, The Canadian Journal of Statistics 2002; 30, 431–439] ignored cross‐product terms in the MSE and hence it is biased. Empirical results on the performance of the proposed MSE estimator are also presented. <jats:italic>The Canadian Journal of Statistics</jats:italic> 38: 598–608; 2010 © 2010 Statistical Society of Canada</jats:p> Mean squared error estimators of small area means using survey weights Canadian Journal of Statistics |
| spellingShingle | Torabi, Mahmoud, Rao, Jon N. K., Canadian Journal of Statistics, Mean squared error estimators of small area means using survey weights, Statistics, Probability and Uncertainty, Statistics and Probability |
| title | Mean squared error estimators of small area means using survey weights |
| title_full | Mean squared error estimators of small area means using survey weights |
| title_fullStr | Mean squared error estimators of small area means using survey weights |
| title_full_unstemmed | Mean squared error estimators of small area means using survey weights |
| title_short | Mean squared error estimators of small area means using survey weights |
| title_sort | mean squared error estimators of small area means using survey weights |
| title_unstemmed | Mean squared error estimators of small area means using survey weights |
| topic | Statistics, Probability and Uncertainty, Statistics and Probability |
| url | http://dx.doi.org/10.1002/cjs.10078 |