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Shrinkage estimation in elliptically contoured distribution with restricted parameter space

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  • Tsukuma Hisayuki

Abstract

This paper deals with the problem of estimating the mean vector of an elliptically contoured distribution with unknown scale matrix, where the mean vector is restricted to an unbounded and closed convex set with a smooth or a piecewise smooth boundary. A shrinkage-type estimator is shown to be better than the maximum likelihood estimator subject to the restriction relative to a quadratic loss.

Suggested Citation

  • 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.
    • Handle: RePEc:bpj:strimo:v:27:y:2009:i:1:p:25-35:n:2
    DOI: 10.1524/stnd.2009.1010
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    References listed on IDEAS

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    1. 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.
    2. Hartigan, J. A., 2004. "Uniform priors on convex sets improve risk," Statistics & Probability Letters, Elsevier, vol. 67(4), pages 285-288, May.
    3. Amirdjanova, Anna & Woodroofe, Michael, 2004. "Shrinkage estimation for convex polyhedral cones," Statistics & Probability Letters, Elsevier, vol. 70(1), pages 87-94, October.
    4. Kubokawa, T. & Srivastava, M. S., 2001. "Robust Improvement in Estimation of a Mean Matrix in an Elliptically Contoured Distribution," Journal of Multivariate Analysis, Elsevier, vol. 76(1), pages 138-152, January.
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    Cited by:

    1. 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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