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Abu-Shanab, R; Veretennikov, AY (2015)
Publisher: American Mathematical Society
Languages: English
Types: Article
Subjects:
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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    • 5. Reman Abu-Shanab, Information Inequalities and Parameter Estimation, PhD Thesis, University of Leeds, UK, 2009.
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    • 8. M. P. Schu¨tzenberger, A propos de l'in´egalit´e de Fr´echet-Cram´er, Publ. Inst. Statist. Univ. Paris 7 (1958), no. 3/4, 3-6; http://igm.univ-mlv.fr/~berstel/Mps/Travaux/A/ 1958FrechetInstStat.pdf
    • 9. H. van Trees, Detection, Estimation and Modulation Theory, vol. I, Wiley, New York, 1968.
    • 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: 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:
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