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Teoriya Veroyatnostei i ee Primeneniya, 1981, Volume 26, Issue 1, Pages 15–31 (Mi tvp2448)  

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

On the correctness of statistical point estimation problem

N. N. Čencov

Moscow
Abstract: Strongly consistent (in the sense of convergence in variation) decision procedures $\Pi=\{\Pi_N\}$ for the statistical point estimation problem are considered. We prove that the statistical problem of estimation the probability distribution $P$ on $E=\{x\colon 0\le x\le 1\}$ by means of independent $P$-distributed bservations $x_i^*$ ($i=1,\dots,N$, $N\to\infty$) without additional a priori information about $P$ is incorrect in this sense. The unknown $P$ being a priori absolutely continuous, the problem turns out to be correct [15]. However this modified problem is found not to admit the uniformly consistent decision procedures. Also it does not admit the procedures with vanishing (at $N\to\infty$) supremum of the risk, when a loss function is given by a Kullback information deviation $I[P_N^*:P]$.
Received: 15.12.1979
English version:
Theory of Probability and its Applications, 1981, Volume 26, Issue 1, Pages 13–29
DOI: https://doi.org/10.1137/1126002
Bibliographic databases:
Language: Russian
Citation: N. N. Čencov, “On the correctness of statistical point estimation problem”, Teor. Veroyatnost. i Primenen., 26:1 (1981), 15–31; Theory Probab. Appl., 26:1 (1981), 13–29
Citation in format AMSBIB
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\by N.~N.~{\v C}encov
\paper On the correctness of statistical point estimation problem
\jour Teor. Veroyatnost. i Primenen.
\yr 1981
\vol 26
\issue 1
\pages 15--31
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=605633}
\zmath{https://zbmath.org/?q=an:0506.62004|0459.62002}
\transl
\jour Theory Probab. Appl.
\yr 1981
\vol 26
\issue 1
\pages 13--29
\crossref{https://doi.org/10.1137/1126002}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1981MY89200002}
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  • https://www.mathnet.ru/eng/tvp/v26/i1/p15
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теория вероятностей и ее применения Theory of Probability and its Applications
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