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Estimation of a parameter vector restricted to a cone

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  • Ouassou, Idir
  • Strawderman, William E.
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    Abstract

    We study estimation of a location vector restricted to a convex cone when the dimension, p, is at least 3. We find estimators which improve on the "usual" estimator (the MLE in the normal case) in the general case of a spherically symmetric distribution with unknown scale. The improved estimators may be viewed as Stein-type shrinkage estimators on the set where the usual unbiased estimator (in the unrestricted case) satisfies the restriction. The improved procedures have the extremely strong property of improving on the "usual" estimator uniformly and simultaneously for all spherically symmetric distributions.

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    File URL: http://www.sciencedirect.com/science/article/B6V1D-44B23XF-2/2/19a45246f155ac86ad19127daf204f63
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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 56 (2002)
    Issue (Month): 2 (January)
    Pages: 121-129

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    Handle: RePEc:eee:stapro:v:56:y:2002:i:2:p:121-129

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    Related research

    Keywords: Stein Estimation Minimaxity Restricted parameter spaces;

    References

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    1. Cellier, D. & Fourdrinier, D., 1995. "Shrinkage Estimators under Spherical Symmetry for the General Linear Model," Journal of Multivariate Analysis, Elsevier, vol. 52(2), pages 338-351, February.
    2. Fourdrinier, Dominique & Strawderman, William E., 1996. "A Paradox Concerning Shrinkage Estimators: Should a Known Scale Parameter Be Replaced by an Estimated Value in the Shrinkage Factor?," Journal of Multivariate Analysis, Elsevier, vol. 59(2), pages 109-140, November.
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    Cited by:
    1. Amirdjanova, Anna & Woodroofe, Michael, 2004. "Shrinkage estimation for convex polyhedral cones," Statistics & Probability Letters, Elsevier, vol. 70(1), pages 87-94, October.
    2. Dominique Fourdrinier & William Strawderman & Martin Wells, 2006. "Estimation of a Location Parameter with Restrictions or “vague information” for Spherically Symmetric Distributions," Annals of the Institute of Statistical Mathematics, Springer, vol. 58(1), pages 73-92, March.
    3. 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.

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