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

2018/04/26 by Tsubasa Ito, Ito, Tsubasa, Tatsuya Kubokawa +1
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1804.10032

openalex publication_date 2018/04/26 · openalex created_date 2018/05/07 · openalex updated_date 2026/07/28

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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