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Estimating one of two normal means when their difference is bounded

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  • van Eeden, Constance
  • V. Zidek, James

Abstract

In this paper, we address the problem of estimating [theta]1 when , are observed, the [sigma]j are known and [theta]1-[theta]2[less-than-or-equals, slant]c for a known constant c. Assuming the loss is squared error, we derive a generalized Bayes estimator which is admissible. It uses Y2 to achieve a uniformly smaller risk than that of the classical UMVU estimator, Y1. The proofs use a combination of Stein and Kubokawa methods.

Suggested Citation

  • van Eeden, Constance & V. Zidek, James, 2001. "Estimating one of two normal means when their difference is bounded," Statistics & Probability Letters, Elsevier, vol. 51(3), pages 277-284, February.
    • Handle: RePEc:eee:stapro:v:51:y:2001:i:3:p:277-284
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    References listed on IDEAS

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    1. Pal N. & Kushary D., 1992. "On Order Restricted Location Parameters Of Two Exponential Distributions," Statistics & Risk Modeling, De Gruyter, vol. 10(1-2), pages 133-152, February.
    2. Tatsuya Kubokawa, 1994. "Double shrinkage estimation of ratio of scale parameters," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(1), pages 95-116, March.
    3. Amarjot Kaur & Harshinder Singh, 1991. "On the estimation of ordered means of two exponential populations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(2), pages 347-356, June.
    4. Kushary D. & Cohen A., 1989. "Estimating Ordered Location And Scale Parameters," Statistics & Risk Modeling, De Gruyter, vol. 7(3), pages 201-214, March.
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    Cited by:

    1. Constantine E. Frangakis & Hao Wu, 2007. "The geometry of inadmissibility of independent observations for estimating a single parameter in two-parameter ordered symmetric problems," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 363-370.
    2. van Eeden, Constance & Zidek, James V., 2004. "Combining the data from two normal populations to estimate the mean of one when their means difference is bounded," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 19-46, January.

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