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Universal estimators of a vector parameter

Author

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  • Rukhin, A. L.

Abstract

Let x be a random sample with a distribution depending on a vector parameter [theta] [set membership, variant] m. The description of distributions and generalized prior densities on m is given, for which the generalized Bayes estimator of [theta], based on x, is the same for all symmetric loss functions. These distributions form a special subclass of exponential family. The specification of this result for the case of a location parameter is considered. The proof of the main theorem is based on the solution of a functional equation of D'Alembert's type.

Suggested Citation

  • Rukhin, A. L., 1984. "Universal estimators of a vector parameter," Journal of Multivariate Analysis, Elsevier, vol. 14(2), pages 135-154, April.
    • Handle: RePEc:eee:jmvana:v:14:y:1984:i:2:p:135-154
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