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On asymptotic Borovkov-Sakhanenko inequality with unbounded parameter set. (English) Zbl 1325.62052

Theory Probab. Math. Stat. 90, 1-12 (2015); translation from Teor. Jmovirn. Mat. Stat. 90, 1–12 (2014).
Summary: Integral analogues of Cramér-Rao’s inequalities for Bayesian parameter estimators proposed initially by M. P. Schutzenberger [Publ. Inst. Stat. Univ. Paris 7, No. 3–4, 3–6 (1959; Zbl 0084.15201)] and later by H. L. Van Trees [Detection, estimation, and modulation theory. Part I. Sydney: John Wiley and Sons, Inc. (1968; Zbl 0202.18002)] were further developed by A. A. Borovkov and A. I. Sakhanenko [Probab. Math. Stat. 1, 185–195 (1980; Zbl 0507.62024)]. 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 \(\mathbb{R}^1\) as a parameter set. Optimality of Borovkov-Sakhanenko’s asymptotic lower bound functional is established.

MSC:

62F12 Asymptotic properties of parametric estimators
62F15 Bayesian inference
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References:

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