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On Bayes estimates

Author

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  • Strasser, Helmut

Abstract

In this paper the author tries to give general conditions for the existence of Bayes estimates and for the consistency of sequences of Bayes estimates. In Section 3 we prove existence theorems for Bayes estimates, which contain those of [3], as a special case. The proof is based on a theorem of [5]. Section 4 gives a characterization of Bayes estimates with convex loss and linear decision space. This theorem is also a generalization of a similar theorem of [3]. In Section 5 we generalize the theory of minimum contrast estimates (the foundations of which were laid by [4], cf. [6]) in such a way that we can apply it to the theory of Bayes estimates. Section 6 tries to give a general theory of consistency for Bayes estimates using the martingale argument of [1] and the theory of minimum contrast estimates. Confer in this connection the results of [8]. Section 7 contains some auxiliary results.

Suggested Citation

  • Strasser, Helmut, 1973. "On Bayes estimates," Journal of Multivariate Analysis, Elsevier, vol. 3(3), pages 293-310, September.
    • Handle: RePEc:eee:jmvana:v:3:y:1973:i:3:p:293-310
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    Cited by:

    1. Abraham, Christophe, 2001. "Asymptotic Limit of the Bayes Actions Set Derived from a Class of Loss Functions," Journal of Multivariate Analysis, Elsevier, vol. 79(2), pages 251-274, November.
    2. Abraham, Christophe, 2005. "Asymptotics in Bayesian decision theory with applications to global robustness," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 50-65, July.

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