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Teor. Veroyatnost. i Primenen., 1973, Volume 18, Issue 1, Pages 78–93 (Mi tvp2682)  

This article is cited in 3 scientific papers (total in 3 papers)

Asymptotical behaviour of some statistical estimators. II. Limiting theorems for the a posteriory density and Bayesian estimators

I. A. Ibragimov, R. Z. Khas'minskii

Moscow

Abstract: In the second part of the paper we use propositions, methods and results of the first part appeared in the previous issue of this journal.
Under conditions I–IV of § 1, we prove theorems about behaviour of the a posteriory density (similar to the well-known Le Cam's results [2]), Bayesian estimators $t_n^{(a)}$ for the risk function $\|\theta\|^a$, Pitman's estimators of the location parameter etc. We prove, for example, that the estimators $t_n^{(a)}$, for different $a\ge1$, are equivalent in the sense that
$$ \mathbf E\{\sqrt n|t_n^{(a_1)}-t_n^{(a_2)}|\}^p\underset{n\to\infty}\longrightarrow0\quad(p>0). $$


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English version:
Theory of Probability and its Applications, 1973, 18:1, 76–91

Bibliographic databases:

Received: 05.01.1971

Citation: I. A. Ibragimov, R. Z. Khas'minskii, “Asymptotical behaviour of some statistical estimators. II. Limiting theorems for the a posteriory density and Bayesian estimators”, Teor. Veroyatnost. i Primenen., 18:1 (1973), 78–93; Theory Probab. Appl., 18:1 (1973), 76–91

Citation in format AMSBIB
\Bibitem{IbrKha73}
\by I.~A.~Ibragimov, R.~Z.~Khas'minskii
\paper Asymptotical behaviour of some statistical estimators. II.~Limiting theorems for the a posteriory density and Bayesian estimators
\jour Teor. Veroyatnost. i Primenen.
\yr 1973
\vol 18
\issue 1
\pages 78--93
\mathnet{http://mi.mathnet.ru/tvp2682}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=311009}
\zmath{https://zbmath.org/?q=an:0283.62038}
\transl
\jour Theory Probab. Appl.
\yr 1973
\vol 18
\issue 1
\pages 76--91
\crossref{https://doi.org/10.1137/1118006}


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    This publication is cited in the following articles:
    1. I. A. Ibragimov, R. Z. Khas'minskii, “Asymptotic behavior of statistical estimates for samples with a discontinuous density”, Math. USSR-Sb., 16:4 (1972), 573–606  mathnet  crossref  mathscinet  zmath
    2. A. A. Zaikin, “Asymptotic expansion of posterior distribution of parameter centered by a $\sqrt n$-consistent estimate”, J. Math. Sci. (N. Y.), 229:6 (2018), 678–697  mathnet  crossref  mathscinet
    3. A. A. Zaikin, “Estimates with asymptotically uniformly minimal $d$-risk”, Theory Probab. Appl., 63:3 (2019), 500–505  mathnet  crossref  crossref  isi  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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