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

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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.

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Authors and Affiliations

  1. Faculty of Medicine, Toho University, 5-21-16 Omori-nishi, Ota-ku, Tokyo, 143-8540, Japan

    Hisayuki Tsukuma

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  1. Hisayuki Tsukuma
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Correspondence to Hisayuki Tsukuma.

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Tsukuma, H. Simultaneous estimation of restricted location parameters based on permutation and sign-change. Stat Papers 53, 915–934 (2012). https://doi.org/10.1007/s00362-011-0396-z

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  • DOI: https://doi.org/10.1007/s00362-011-0396-z

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