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Non-minimaxity of Linear Combinations of Restricted Location Estimators and Related Problems

Author

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  • Tatsuya Kubokawa

    (Faculty of Economics, University of Tokyo)

  • William E. Strawderman

    (Department of Statistics, Rutgers University)

Abstract

The estimation of a linear combination of several restricted location parameters is addressed from a decision-theoretic point of view. The corresponding linear combination of the best location equivariant and the unrestricted unbiased estimators is minimax. Since the locations are restricted, it is reasonable to use the linear combination of the restricted estimators such as maximum likelihood estimators. In this paper, a necessary and sufficient condition for such restricted estimators to be minimax is derived, and it is shown that the restricted estimators are not minimax when the number of the location parameters is large. The condition for the minimaxity is examined for some specific distributions. Finally, similar problems of estimating the product and sum of the restricted scale parameters are studied, and it is shown that similar non-dominance properties appear when the number of the scale parameters is large.

Suggested Citation

  • Tatsuya Kubokawa & William E. Strawderman, 2010. "Non-minimaxity of Linear Combinations of Restricted Location Estimators and Related Problems," CIRJE F-Series CIRJE-F-749, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2010cf749
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    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2010/2010cf749.pdf
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    References listed on IDEAS

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    1. Tsukuma, Hisayuki & Kubokawa, Tatsuya, 2008. "Stein's phenomenon in estimation of means restricted to a polyhedral convex cone," Journal of Multivariate Analysis, Elsevier, vol. 99(1), pages 141-164, January.
    2. Éric Marchand & William Strawderman, 2005. "Improving on the minimum risk equivariant estimator of a location parameter which is constrained to an interval or a half-interval," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(1), pages 129-143, March.
    3. Hartigan, J. A., 2004. "Uniform priors on convex sets improve risk," Statistics & Probability Letters, Elsevier, vol. 67(4), pages 285-288, May.
    4. Tatsuya Kubokawa, 2004. "Minimaxity in Estimation of Restricted Parameters," CIRJE F-Series CIRJE-F-270, CIRJE, Faculty of Economics, University of Tokyo.
    5. Tatsuya Kubokawa, 2010. "Minimax Estimation of Linear Combinations of Restricted Location Parameters," CIRJE F-Series CIRJE-F-723, CIRJE, Faculty of Economics, University of Tokyo.
    Full references (including those not matched with items on IDEAS)

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