CONSTRAINED MINIMAX ESTIMATION OF THE MEAN OF THE NORMAL-DISTRIBUTION WITH KNOWN VARIANCE
成果类型：
Note
署名作者：
FELDMAN, I
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/aos/1176348398
发表日期：
1991
页码：
2259-2265
关键词：
摘要：
In this paper we shall discuss the estimation of the mean of a normal distribution with variance 1. The main question in this work is the existence and computation of a least favorable distribution among all the prior distributions satisfying a given set of constraints. In the following we show that if this distribution is bounded from above on some even moment, then the least favorable distribution exists and it is either normal or discrete. The support of the discrete distribution function does not have any accumulation point. The least favorable distribution is normal if and only if the second moment is bounded from above, without any other relevant constraint. These theorems shed light on the James-Stein estimator as the mini-max estimator for a prior with unknown bounded variance.