Improving on the positive part of the umvue of a noncentrality parameter of a noncentral chi-square distribution

Peter Yi Shi Shao, William E. Strawderman

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Abstract

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.

Original languageEnglish (US)
Pages (from-to)52-66
Number of pages15
JournalJournal of Multivariate Analysis
Volume53
Issue number1
DOIs
StatePublished - Apr 1995

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

Keywords

  • Admissibility
  • Squared error loss

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