Corrected empirical Bayes confidence region in a multivariate Fay–Herriot model

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 small area. For measuring uncertainty of EBLUP, much of research is focused on second-order unbiased 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 region of the small area mean that is based on the Mahalanobis distance centered around EBLUP and has second-order correction. 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.