Information Inequalities for the Bayes Risk
Lawrence D. Brown, Leslaw Gajek
The Annals of Statistics · 1990 · Volume 18 · Issue 4
Abstract
This paper presents lower bounds, derived from the information inequality, for the Bayes risk under scaled quadratic loss. Some numerical results are also presented which give some idea concerning the precision of these bounds. An appendix contains a proof of the information inequality without conditions on the estimator. This result is a direct extension of an earlier result of Fabian and Hannan.
Keywords
60E15, 62C99, 62F10, 62F15, Bayes risk, exponential family, Information inequality (Cramer-Rao inequality)
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