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

• Published in: Journal of multivariate analysis 1995-04, Vol.53 (1), p.52-66
• Main Authors: Shao, P.Y.S., Strawderman, W.E.
• Format: Article
• Language: English
• Subjects: Decision theory; Exact sciences and technology; Mathematics; Multivariate analysis; Parametric inference; Probability and statistics; Sciences and techniques of general use; Statistics
• ISSN: 0047-259X; 1095-7243
• DOI: 10.1006/jmva.1995.1024

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 χ 2 n (μ/2). Let Y ∼ χ 2 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.