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Teor. Veroyatnost. i Primenen., 1972, Volume 17, Issue 3, Pages 469–486 (Mi tvp2659)  

This article is cited in 4 scientific papers (total in 4 papers)

Asymptotical behavior of some statistical estimators in the smooth case. I. Study of the likelihood ratio

I. A. Ibragimova, R. Z. Khas'minskiib

a Leningrad
b Moscow

Abstract: The paper considers properties of likelihood ratio determined by (1.1). We prove that the distributions in functional space $\mathbf C_0$, generated by the processes $Z_n(\theta)$ $(-\infty<\theta<\infty)$ tend to the distribution in $\mathbf C_0$, generated by the process $Z(\theta)$ defined by (2.1), provided conditions I–IV of section 1 are satisfied. As a consequence, we have asymptotical normality of the maximum likelihood estimator without assumptions of continuity of $\log f(x,\theta)$ and existence of $f"_{\theta\theta}(x,\theta)$. We deduce several other consequences of this result useful in the second part of the paper.

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English version:
Theory of Probability and its Applications, 1973, 17:3, 445–462

Bibliographic databases:

Received: 05.01.1971

Citation: I. A. Ibragimov, R. Z. Khas'minskii, “Asymptotical behavior of some statistical estimators in the smooth case. I. Study of the likelihood ratio”, Teor. Veroyatnost. i Primenen., 17:3 (1972), 469–486; Theory Probab. Appl., 17:3 (1973), 445–462

Citation in format AMSBIB
\Bibitem{IbrKha72}
\by I.~A.~Ibragimov, R.~Z.~Khas'minskii
\paper Asymptotical behavior of some statistical estimators in the smooth case. I.~Study of the likelihood ratio
\jour Teor. Veroyatnost. i Primenen.
\yr 1972
\vol 17
\issue 3
\pages 469--486
\mathnet{http://mi.mathnet.ru/tvp2659}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=311008}
\zmath{https://zbmath.org/?q=an:0273.62019}
\transl
\jour Theory Probab. Appl.
\yr 1973
\vol 17
\issue 3
\pages 445--462
\crossref{https://doi.org/10.1137/1117054}


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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. M. V. Burnashev, “Investigation of second order properties of statistical estimators in a scheme of independent observations”, Math. USSR-Izv., 18:3 (1982), 439–467  mathnet  crossref  mathscinet  zmath
    3. 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
    4. 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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