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 χ²_n(μ/2). Let Y ∼ χ²_n(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.