Estimation of the Non-Centrality Parameter of a Chi Squared Distribution

Abstract

Let $X$ be distributed according to a non-central Chi squared distribution with $p$ degrees of freedom. The non-central Chi squared distribution arises in various statistical analyses and the estimation of the non-centrality parameter is of importance in some problems. This paper deals with the admissibility of certain estimates of the non-centrality parameter. It is shown that $(X - p)^+$, the positive part of $X - p$ dominates the maximum likelihood estimator with squared error as the loss function.