Title: A wider class of estimators of positive normal means, individual and simultaneity
Authors: Genso-Y. T. Watanabe-Chang - Mejiro University (Japan) [presenting]
Nobuo Shinozaki - Keio University (Japan)
Abstract: While estimating a positive normal mean, $\theta$, when variance is unknown, it has been shown that the Bayes estimator is a minimax and admissible estimator based on uniform prior on [0, $\infty$) of $\theta$ under squared error loss. We propose a generalized Bayes estimator based on gamma prior distribution for $\theta$. The proposed generalized Bayes estimator includes the previous estimator and is an admissible estimator of positive normal mean. Based on the proposed generalized Bayes estimator, we consider the Stein-type estimator for estimation $p$ unknown non-negative normal means, simultaneously, and give a sufficient condition for proposed Stein-type estimators dominate the generalized Bayes estimators under sum of squared error loss.