Improving on the Positive Part of the UMVUE of a Noncentrality Parameter of a Noncentral Chi-Square Distribution

The purpose of this paper is to give an explicit estimator dominating the positive part of the UMVUE of a noncentrality parameter of a noncentral χ2n(μ/2). Let Y ∼ χ2n(μ/2) with degree of freedom n and unknown parameter μ, loss = (δ − μ)2. In his (1974) paper de Waal showed that Y + n is the generalized Bayes estimator of μ with respect to a noninformative prior distribution (Comm. Statist.3(1), 73-79). Y − n is the UMVUE of μ and dominates Y + n, but is dominated by (Y − n)+. Alam and Saxena (1982, Ann. Statist.10, 1012-1016) showed that (Y − n)+ dominates the MLE of μ. Chow (1987, Ann. Statist.15, 800-804) showed that (Y − n)+ is inadmissible. Explicit improvements, however, have not previously been found.