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Theory of Probability and Mathematical Statistics
(Teoriya Imovirnostei ta Matematychna Statystyka)



On asymptotic Borovkov–Sakhanenko inequality with unbounded parameter set

R. Abu-Shanab, A. Yu. Veretennikov

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Abstract: Integral analogues of Cramér-Rao's inequalities for Bayesian parameter estimators proposed initially by Schützenberger (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 R as a parameter set. Optimality of Borovkov-Sakhanenko's asymptotic lower bound functional is established.

Keywords: Cramér-Rao bounds, Borovkov-Sakhanenko bounds, integral information inequalities, asymptotic efficiency

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