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

✍ Scribed by P.Y.S. Shao; W.E. Strawderman

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 344 KB
• Volume: 53
• Category: Article
• ISSN: 0047-259X
• DOI: 10.1006/jmva.1995.1024

✦ Synopsis

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_{n}^{2}(\mu 2)). Let (Y \sim \chi_{n}^{2}(\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. Staist. 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, Am. Statist. 10, 1012-1016) showed that ((Y-n)). dominates the MLE of (\mu). Chow (1987. Am. Statist. 15, 800 804) showed that ((Y-n)). is inadmissible. Explicit improvements. however. have not previously been found. 11949 Acadenic Press. Inc.