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Information inequalities for the Bayes risk. (English) Zbl 0722.62003

A series of lower bounds for the Bayes risk of an estimator \({\hat \theta}\) of a real parameter \(\theta\) under loss m(\(\theta\))(\({\hat \theta}\)-\(\theta\))\({}^ 2\), \(m(\theta)>0\) is given. Five nontrivial examples illustrate the accuracy of the bounds. The results are based on a version of the information inequality without regularity conditions on the statistic under consideration. The statement and the proof of the inequality are also given.

MSC:

62C10 Bayesian problems; characterization of Bayes procedures
62F10 Point estimation
62F15 Bayesian inference
62C99 Statistical decision theory
60E15 Inequalities; stochastic orderings
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