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Simultaneous estimation of restricted location parameters based on permutation and sign-change

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  • Hisayuki Tsukuma

Abstract

The problem of simultaneously estimating location parameters is addressed, where the vector of location parameters belongs to a polyhedral cone including simple order, tree order and positive orthant restrictions and so forth. This paper proposes modified estimators based on orthogonal transformations such as sign-change and permutation and proves that, in a multivariate location family, the modified estimators are minimax under quadratic loss. Shrinkage minimax estimators improving on the modified estimators are obtained for a restricted mean vector of spherically symmetric distribution. An application of sign-change transformation is also given in estimation of a bounded normal mean. Copyright Springer-Verlag 2012

Suggested Citation

  • Hisayuki Tsukuma, 2012. "Simultaneous estimation of restricted location parameters based on permutation and sign-change," Statistical Papers, Springer, vol. 53(4), pages 915-934, November.
    • Handle: RePEc:spr:stpapr:v:53:y:2012:i:4:p:915-934
    DOI: 10.1007/s00362-011-0396-z
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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. Tsukuma Hisayuki, 2009. "Shrinkage estimation in elliptically contoured distribution with restricted parameter space," Statistics & Risk Modeling, De Gruyter, vol. 27(1), pages 25-35, November.
    3. Ouassou, Idir & Strawderman, William E., 2002. "Estimation of a parameter vector restricted to a cone," Statistics & Probability Letters, Elsevier, vol. 56(2), pages 121-129, January.
    4. Fourdrinier, Dominique & Ouassou, Idir & Strawderman, William E., 2003. "Estimation of a parameter vector when some components are restricted," Journal of Multivariate Analysis, Elsevier, vol. 86(1), pages 14-27, July.
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