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Teoriya Veroyatnostei i ee Primeneniya, 1974, Volume 19, Issue 2, Pages 340–354 (Mi tvp2855)  

This article is cited in 2 scientific papers (total in 2 papers)

On the behaviour of the generalized Вayes estimates for Markov observations

B. Ya. Levit

Moscow
Full-text PDF (790 kB) Citations (2)
Abstract: We consider the behaviour of the generalized Bayes estimates $\widehat\theta_n$ of an unknown parameter $\theta$ assuming that the observations $X_1,\dots,X_n,\dots$ form a transient Markov chain. It is shown that, under some conditions, the limit distribution of the sequence $\sqrt n(\widehat\theta_n-\theta)$ is a weighted normal law. The main restriction is that there must exist a.s. nonzero limit of the $I(X_n)$, where $I(X)$ is the (conditioned) Fiser information. Some examples show that, if this restriction is not satisfied, the estimation problem becomes “irregular”.
Received: 03.08.1971
English version:
Theory of Probability and its Applications, 1975, Volume 19, Issue 2, Pages 332–346
DOI: https://doi.org/10.1137/1119037
Bibliographic databases:
Language: Russian
Citation: B. Ya. Levit, “On the behaviour of the generalized Вayes estimates for Markov observations”, Teor. Veroyatnost. i Primenen., 19:2 (1974), 340–354; Theory Probab. Appl., 19:2 (1975), 332–346
Citation in format AMSBIB
\Bibitem{Lev74}
\by B.~Ya.~Levit
\paper On the behaviour of the generalized Вayes estimates for Markov observations
\jour Teor. Veroyatnost. i Primenen.
\yr 1974
\vol 19
\issue 2
\pages 340--354
\mathnet{http://mi.mathnet.ru/tvp2855}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=370975}
\zmath{https://zbmath.org/?q=an:0334.62033}
\transl
\jour Theory Probab. Appl.
\yr 1975
\vol 19
\issue 2
\pages 332--346
\crossref{https://doi.org/10.1137/1119037}
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  • https://www.mathnet.ru/eng/tvp/v19/i2/p340
  • This publication is cited in the following 2 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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