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On asymptotic Borovkov-Sakhanenko inequality with unbounded parameter set

Authors: R. Abu-Shanab and A. Yu. Veretennikov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 90 (2014).
Journal: Theor. Probability and Math. Statist. 90 (2015), 1-12
MSC (2010): Primary 62F12, 62F15
Published electronically: August 6, 2015
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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 $ \mathbf {R}^1$ as a parameter set. Optimality of Borovkov-Sakhanenko's asymptotic lower bound functional is established.

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Additional Information

R. Abu-Shanab
Affiliation: P.O. Box 32038, Department of Mathematics, College of Science, University of Bahrain, Kingdom of Bahrain

A. Yu. Veretennikov
Affiliation: School of Mathematics, University of Leeds, LS2 9JT, United Kingdom & Institute for Information Transmission Problems, Moscow, Russia – and – National Research University Higher School of Economics, Moscow, Russia

Keywords: Cram\'er--Rao bounds, Borovkov--Sakhanenko bounds, integral information inequalities, asymptotic efficiency
Received by editor(s): November 1, 2013
Published electronically: August 6, 2015
Additional Notes: The paper is based on a chapter in the first author’s PhD Thesis \cite{Reman}. Both authors are grateful to Professor Sakhanenko for his comments. The second author’s work was partially supported by RFBR grant 13-01-12447 ofi_m2.
Article copyright: © Copyright 2015 American Mathematical Society

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