Corrected Empirical Bayes Confidence Region in a Multivariate Fay-Herriot Model

Tsubasa Ito; Tatsuya Kubokawa

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arXiv · 1804.10032

Corrected Empirical Bayes Confidence Region in a Multivariate Fay-Herriot Model

Tsubasa Ito·Tatsuya Kubokawa

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Abstract

In the small area estimation, the empirical best linear unbiased predictor (EBLUP) in the linear mixed model is useful because it gives a stable estimate for a mean of a smallarea. For measuring uncertainty of EBLUP, much of research is focused on second-orderunbiased estimation of mean squared prediction errors in the univariate case. In this paper, we consider the multivariate Fay-Herriot model where the covariance matrix of random effects is fully unknown, and obtain a confidence reagion of the small area mean that is based on the Mahalanobis distance centered around EBLUP and is second order correct. A positive-definite, consistent and second-order unbiased estimator of the covariance matrix of the random effects is also suggested. The performance is investigated through simulation study.

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Tsubasa Ito, Tatsuya Kubokawa. 2018-04-26. Corrected Empirical Bayes Confidence Region in a Multivariate Fay-Herriot Model. https://arxiv.org/abs/1804.10032

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