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Stein estimation for non-normal spherically symmetric location families in three dimensions

Author

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  • Ralescu, Stefan
  • Brandwein, Ann Cohen
  • Strawderman, William E.

Abstract

We consider estimation of a location vector in the presence of known or unknown scale parameter in three dimensions. The technique of proof is Stein's integration by parts and it is used to cover several cases (e.g., non-unimodal distributions) for which previous results were known only in the cases of four and higher dimensions. Additionally, we give a necessary and sufficient condition on the shrinkage constant for improvement on the usual estimator for the spherical uniform distribution.

Suggested Citation

  • Ralescu, Stefan & Brandwein, Ann Cohen & Strawderman, William E., 1992. "Stein estimation for non-normal spherically symmetric location families in three dimensions," Journal of Multivariate Analysis, Elsevier, vol. 42(1), pages 35-50, July.
    • Handle: RePEc:eee:jmvana:v:42:y:1992:i:1:p:35-50
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    Cited by:

    1. Fourdrinier, Dominique & Lemaire, Anne-Sophie, 2002. "Estimation under l1-Symmetry," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 303-323, November.
    2. He Kun & Strawderman William E., 2001. "Estimation In Spherically Symmetric Regression With Random Design," Statistics & Risk Modeling, De Gruyter, vol. 19(1), pages 41-50, January.

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