小地域推定におけるモデル分散パラメーターに対する0推定値の発生とその回避法

Open House, ISM in Tachikawa, 2016.6.17統計数理研究所オープンハウス（立川）、H28.6.17ポスター発

An adjusted maximum likelihood method for solving small area estimation problems

For the well-known Fay-Herriot small area model, standard variance component estimation methods frequently produce zero estimates of the strictly positive model variance. As a consequence, an empirical best linear unbiased predictor of a small area mean, commonly used in small area estimation, could reduce to a simple regression estimator, which typically has an overshrinking problem. We propose an adjusted maximum likelihood estimator of the model variance that maximizes an adjusted likelihood defined as a product of the model variance and a standard likelihood (e.g., a profile or residual likelihood) function. The adjustment factor was suggested earlier by Carl Morris in the context of approximating a hierarchical Bayes solution where the hyperparameters, including the model variance, are assumed to follow a prior distribution. Interestingly, the proposed adjustment does not affect the mean squared error property of the model variance estimator or the corresponding empirical best linear unbiased predictors of the small area means in a higher order asymptotic sense. However, as demonstrated in our simulation study, the proposed adjustment has a considerable advantage in small sample inference, especially in estimating the shrinkage parameters and in constructing the parametric bootstrap prediction intervals of the small area means, which require the use of a strictly positive consistent model variance estimate.Adjusted density maximization estimator The Fay-Herriot model Parametric bootstrap Prediction intervals

混合効果モデルによる小地域推定へのアプローチ

学位の種別: 論文博士審査委員会委員 : （主査）東京大学教授 久保川 達也, 東京大学教授 大森 裕浩, 東京大学教授 下津 克己, 東京大学准教授 加藤 賢悟, 東京大学講師 入江 薫University of Tokyo(東京大学