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

Non-central chi-squared distribution plays a vital role in commonly used statistical testing procedures. The non-centrality parameter δδ provides valuable information on the power of the associated test. In this paper, based on one observation XX sampled from a chi-squared distribution with pp degrees of freedom and non-centrality parameter δδ, we study a new class of non-centrality parameter estimators δˆβ(X)=max{X−p,βX},0≤β<1, and investigate their statistical properties under the quadratic loss function. Theoretical and simulation studies indicate that δˆ1/(1+p)(X) generally works well compared with other existing estimators, especially for relatively small and moderate δδ.