Mean squared error estimators of small area means using survey weights |
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Authors: | Mahmoud Torabi Jon N K Rao |
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Institution: | 1. Department of Community Health Sciences, University of Manitoba, Winnipeg, Manitoba, Canada R3E 0W3;2. School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada K1S 5B6 |
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Abstract: | 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. The Canadian Journal of Statistics 38: 598–608; 2010 © 2010 Statistical Society of Canada |
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Keywords: | Benchmarking design consistency mean squared error estimation nested error regression model MSC 2000: Primary 62D05 |
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