On estimating the non-centrality parameter of a chi-squared distribution

Abstract

Non-central chi-squared distribution plays a vital role in commonly used statistical testing procedures. The non-centrality parameter δ provides valuable information on the power of the associated test. In this paper, based on one observation X sampled from a chi-squared distribution with p degrees of freedom and non-centrality parameter δ , we study a new class of non-centrality parameter estimators δ ˆ β ( X ) = max { X − p , β X } , 0 ≤ β < 1 , and investigate their statistical properties under the quadratic loss function. Theoretical and simulation studies indicate that δ ˆ 1 / ( 1 + p ) ( X ) generally works well compared with other existing estimators, especially for relatively small and moderate δ .