On asymptotic Borovkov–Sakhanenko inequality with unbounded parameter set

Abstract

Integral analogues of Cramer-Rao's inequalities for Bayesian parameter estimators proposed initially by Schutzenberger (1958) and later by van Trees (1968) were further developed by Borovkov and Sakhanenko (1980). In this paper, new asymptotic versions of such inequalities are established under ultimately relaxed regularity assumptions and under a locally uniform nonvanishing of the prior density and with R1 as a parameter set. Optimality of Borovkov-Sakhanenko's asymptotic lower bound functional is established.