## The Annals of Statistics

### 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.

#### Article information

Source
Ann. Statist., Volume 10, Number 3 (1982), 1012-1016.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176345892

Digital Object Identifier
doi:10.1214/aos/1176345892

Mathematical Reviews number (MathSciNet)
MR663453

Zentralblatt MATH identifier
0485.62006

JSTOR