An Integral Bhattacharyya Type Bound for the Bayes Risk

Abstract

Bhattacharyya type integral inequalities for the integrated risk for estimators are given extending the work of Borovkov and Sakhanienko (1980). As an application, an asymptotic approximation of the lower bound for locally minimax risk is given.

Keywords:

• Bayes risk
• Bhattacharyya type bound
• Borovkov–Sakhanienko type bound
• Cramér–Rao type bound
• Local minimax risk

Mathematics Subject Classification:

• Primary 62F15
• Secondary 62F10

Acknowledgments

The author would like to thank Professor M.\ Akahira for his encouragement throughout the preparation of the article.