Minimax estimators and Gamma-minimax estimators for a bounded normal mean under the loss l_p(\vartheta, d) = | \vartheta - d |^p

Kurzfassung/Abstract

Let the random variable $X$ be normally distributed with known variance $\sigma\sp 2 >0$. It is supposed that the unknown mean $\theta$ is an element of a bounded interval $\Theta$. The problem of estimating $\theta$ under the loss function $l\sb p(\theta,d)=\vert \theta-d\vert\sp p$ where $p\ge 2$ is considered. In case the length of the interval $\Theta$ is sufficiently small the minimax estimator and the $\Gamma(\beta,\tau)$-minimax estimator, where $\Gamma(\beta,\tau)$ represents special vague prior information, are given.