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Improved confidence sets for spherically symmetric distributions

Author

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  • Robert, Christian
  • Casella, George

Abstract

The usual confidence set for a multivariate mean vector can be improved upon by recentering the set at a Stein-type estimator: this fact is known to be true under many different distributional assumptions. Thus far, however, the case of unknown variance has not been dealt with analytically. In this paper we prove that recentered set estimators dominate the usual set estimator when sampling is from any of a class of spherically symmetric distributions with unknown variance.

Suggested Citation

  • Robert, Christian & Casella, George, 1990. "Improved confidence sets for spherically symmetric distributions," Journal of Multivariate Analysis, Elsevier, vol. 32(1), pages 84-94, January.
    • Handle: RePEc:eee:jmvana:v:32:y:1990:i:1:p:84-94
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    Cited by:

    1. Takada, Yoshikazu, 1998. "Asymptotic Improvement of the Usual Confidence Set in a Multivariate Normal Distribution with Unknown Variance," Journal of Multivariate Analysis, Elsevier, vol. 64(2), pages 118-130, February.
    2. Hannes Leeb & Paul Kabaila, 2017. "Admissibility of the usual confidence set for the mean of a univariate or bivariate normal population: the unknown variance case," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(3), pages 801-813, June.

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