Brown, Lawrence D.; Gajek, Leslaw Information inequalities for the Bayes risk. (English) Zbl 0722.62003 Ann. Stat. 18, No. 4, 1578-1594 (1990). 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. Reviewer: R.Zielinski (Warszawa) Cited in 4 ReviewsCited in 18 Documents MSC: 62C10 Bayesian problems; characterization of Bayes procedures 62F10 Point estimation 62F15 Bayesian inference 62C99 Statistical decision theory 60E15 Inequalities; stochastic orderings Keywords:Cramér-Rao inequality; exponential family; scaled quadratic loss; lower bounds; Bayes risk; examples; accuracy; information inequality PDFBibTeX XMLCite \textit{L. D. Brown} and \textit{L. Gajek}, Ann. Stat. 18, No. 4, 1578--1594 (1990; Zbl 0722.62003) Full Text: DOI