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Estimation of location parameters for spherically symmetric distributions

Author

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  • Xu, Jian-Lun
  • Izmirlian, Grant

Abstract

Estimation of the location parameters of a px1 random vector with a spherically symmetric distribution is considered under quadratic loss. The conditions of Brandwein and Strawderman [Ann. Statist. 19(1991) 1639-1650] under which estimators of the form dominate are (i) where -h is superharmonic, (ii) is nonincreasing in R, where has a uniform distribution in the sphere centered at with a radius R, and (iii) . In this paper, we not only drop their condition (ii) to show the dominance of over but also obtain a new bound for a which is sometimes better than that obtained by Brandwein and Strawderman. Specifically, the new bound of a is 0

Suggested Citation

  • Xu, Jian-Lun & Izmirlian, Grant, 2006. "Estimation of location parameters for spherically symmetric distributions," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 514-525, February.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:2:p:514-525
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    References listed on IDEAS

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    1. Bock, M. E., 1985. "Minimax estimators that shift towards a hypersphere for location vectors of spherically symmetric distributions," Journal of Multivariate Analysis, Elsevier, vol. 17(2), pages 127-147, October.
    2. Brandwein, Ann Cohen, 1979. "Minimax estimation of the mean of spherically symmetric distributions under general quadratic loss," Journal of Multivariate Analysis, Elsevier, vol. 9(4), pages 579-588, December.
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