On asymptotic Boronkov-Sakhanenko inequality with unbounded parameter set

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Abu-Shanab, R ; Veretennikov, AY (2015)
  • Publisher: American Mathematical Society

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 R1 as a parameter set. Optimality of Borovkov-Sakhanenko's asymptotic lower bound functional is established.
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    10. A. Yu. Veretennikov, On asymptotic information integral inequalities, Theory of Stochastic Processes 13(29) (2007), no. 1-2, 294-307. P.O.Box 32038, Department of Mathematics, College of Science, University of Bahrain, Kingdom of Bahrain E-mail address: raboshanab@uob.edu.bh School of Mathematics, University of Leeds, LS2 9JT, United Kingdom & Institute for Information Transmission Problems, Moscow, Russia & National Research University Higher School of Economics, Moscow, Russia E-mail address: a.veretennikov@leeds.ac.uk

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