  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.
