On Bayes estimates

Helmut Strasser

Journal of Multivariate Analysis, 1973, vol. 3, issue 3, 293-310

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.

Keywords: Bayes; estimates; existence; theorems; minimum; contrast; estimates; consistency (search for similar items in EconPapers)
Date: 1973
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Citations: View citations in EconPapers (2)

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