J. Japan Statist. Soc., Vol. 34 (No. 1), pp. 65-74, 2004
Abstract. In this paper, the Vincze inequality for the Bayes risk of an estimator with the unbiasedness at any two specific values of the parameter is derived using the Lagrange method. The lower bound for the Bayes risk is also shown to be attained. The Cramér-Rao inequality is derived from the information inequality. Some examples on non-regular distributions are also given.
Key words and phrases: Bayes estimator, Bayes risk, Cramér-Rao inequality, information inequality, Lagrange method, non-regular distributions.