変量効果モデルや混合線形モデルを利用した小地域推定について，経験ベイズ法に基づい た信頼区間で，群の数を大きくしたときに被覆確率が信頼係数に２次漸近近似するものを構成 する。これによって，従来得られてきた信頼区間は，より現実的で一般的なモデルへ拡張され ることになり，シミュレーションによる数値的性質を調べるとともに，地価公示価格の小地域 推定と信頼区間の作成への応用が示される。

This paper addresses the issue of constructing a confidence interval of a small area mean in a random effect or mixed effects linear model. A crude confidence interval based on the empirical Bayes method has the drawback that its coverage probability is much less than a nominal confidence coefficient. For improving on this confidence interval, the paper provides the procedure of adjusting the critical value, and the resulting confidence interval has a coverage probability which is identical to the nominal confidence coefficient in second order asymptotics when the number of small areas is large. The proposed confidence interval is numerically investigated based on simulation experiments and applied to posted land price data. These numerical studies illustrate the practical usefulness of the proposal.