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

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  • Shao, P. Y. S.
  • Strawderman, W. E.

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 [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.

Suggested Citation

  • Shao, P. Y. S. & Strawderman, W. E., 1995. "Improving on the Positive Part of the UMVUE of a Noncentrality Parameter of a Noncentral Chi-Square Distribution," Journal of Multivariate Analysis, Elsevier, vol. 53(1), pages 52-66, April.
    • Handle: RePEc:eee:jmvana:v:53:y:1995:i:1:p:52-66
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    Cited by:

    1. López-Blázquez, F., 2000. "Unbiased Estimation in the Non-central Chi-Square Distribution," Journal of Multivariate Analysis, Elsevier, vol. 75(1), pages 1-12, October.
    2. Simon Vandekar & Ran Tao & Jeffrey Blume, 2020. "A Robust Effect Size Index," Psychometrika, Springer;The Psychometric Society, vol. 85(1), pages 232-246, March.

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