Benchmarked linear shrinkage prediction in the Fay–Herriot small area model |
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Authors: | Kentaro Chikamatsu Tatsuya Kubokawa |
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Institution: | 1. Graduate School of Economics, University of Tokyo, Tokyo, Japan;2. Faculty of Economics, University of Tokyo, Tokyo, Japan |
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Abstract: | The empirical best linear unbiased predictor (EBLUP) is a linear shrinkage of the direct estimate toward the regression estimate and useful for the small area estimation in the sense of increasing precision of estimation of small area means. However, one potential difficulty of EBLUP is that the overall estimate for a larger geographical area based on a sum of EBLUP is not necessarily identical to the corresponding direct estimate like the overall sample mean. To fix this problem, the paper suggests a new method for benchmarking EBLUP in the Fay–Herriot model without assuming normality of random effects and sampling errors. The resulting benchmarked empirical linear shrinkage (BELS) predictor has novelty in the sense that coefficients for benchmarking are adjusted based on the data from each area. To measure the uncertainty of BELS, the second-order unbiased estimator of the mean squared error is derived. |
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Keywords: | benchmark best linear unbiased predictor Fay–Herriot model linear shrinkage mean squared error nonnormal distribution small area estimation |
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