Information inequalities for the Bayes risk (Q756309)

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.