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On the estimation of a restricted normal mean

Author

Listed:
  • Gatsonis, Constantine
  • MacGibbon, Brenda
  • Strawderman, William

Abstract

Let X ~ N([theta],1), where [theta] [epsilon] [-m, m], for some m> 0, and consider the problem of estimating [theta] with quadratic loss. We show that the Bayes estimator [delta]m, corresponding to the uniform prior on [-m, m], dominates [delta]0 (x) = x on [-m, m] and it also dominates the MLE over a large part of the parameter interval. We further offer numerical evidence to suggest that [delta]m has quite satisfactory risk performance when compared with the minimax estimators proposed by Casella and Strawderman (1981) and the estimators proposed by Bickel (1981).

Suggested Citation

  • Gatsonis, Constantine & MacGibbon, Brenda & Strawderman, William, 1987. "On the estimation of a restricted normal mean," Statistics & Probability Letters, Elsevier, vol. 6(1), pages 21-30, September.
    • Handle: RePEc:eee:stapro:v:6:y:1987:i:1:p:21-30
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    Citations

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    Cited by:

    1. Somesh Kumar & Yogesh Tripathi, 2008. "Estimating a restricted normal mean," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 68(3), pages 271-288, November.
    2. Droge, Bernd, 2006. "Minimax regret comparison of hard and soft thresholding for estimating a bounded normal mean," Statistics & Probability Letters, Elsevier, vol. 76(1), pages 83-92, January.
    3. Hartigan, J. A., 2004. "Uniform priors on convex sets improve risk," Statistics & Probability Letters, Elsevier, vol. 67(4), pages 285-288, May.
    4. Marchand Éric & MacGibbon Brenda, 2000. "Minimax Estimation Of A Constrained Binomial Proportion," Statistics & Risk Modeling, De Gruyter, vol. 18(2), pages 129-168, February.

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