In the small area estimation, the empirical best linear unbiased predictor (EBLUP)
or the empirical Bayes estimator (EB) in the linear mixed model is recognized useful
because it gives a stable and reliable estimate for a mean of a small area. In practical
situations where EBLUP is applied to real data, it is important to evaluate how
much EBLUP is reliable. One method for the purpose is to construct a confidence
interval based on EBLUP. In this paper, we obtain an asymptotically corrected empirical
Bayes confidence interval in a nested error regression model with unbalanced
sample sizes and unknown components of variance. The coverage probability is
shown to satisfy the confidence level in the second order asymptotics. It is numerically
revealed that the corrected confidence interval is superior to the conventional
confidence interval based on the sample mean in terms of the coverage probability
and the expected width of the interval. Finally, it is applied to the posted land
price data in Tokyo and the neighboring prefecture.
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