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 [chi]2n([mu]/2). Let Y ~ [chi]2n([mu]/2) with degree of freedom n and unknown parameter [mu], LOSS = ([delta] - [mu])2. In his (1974) paper de Waal showed that Y + n is the generalized Bayes estimator of [mu] with respect to a noninformative prior distribution (Comm. Statist.3(1), 73-79). Y - n is the UMVUE of [mu] 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 [mu]. Chow (1987, Ann. Statist.15, 800-804) showed that (Y - n)+ is inadmissible. Explicit improvements, however, have not previously been found.