RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Teor. Veroyatnost. i Primenen.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Teor. Veroyatnost. i Primenen., 1973, Volume 18, Issue 2, Pages 303–311 (Mi tvp4248)  

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

An Asymptotic Expansion for a Class of Estimators Containing Maximum Likelihood Estimators

D. M. Chibisov

Moscow

Abstract: Let $X_1,…,X_n$ be a sample from a distribution dependent on a parameter $\theta=(\theta_1,…,\theta_s)^T$ and $\vartheta_n=\vartheta_n(X_1,…,X_n)$ a minimum contrast estimator for $\theta$ corresponding to a contrast function $f(x,\theta)$ (see, e.g., [7], [8], [9]). When the $X_i$'s have a density $p(x,\theta)$ and $f(x,\theta)=-\log p(x,\theta), \vartheta$ is the maximum likelihood estimator. Among the regularity conditions, it is assumed that the continous derivatives $f^{\alpha}(x,\theta)=(d^{\alpha_1+…+\alpha_s}/d\theta_1^{\alpha_1}…d\theta_s^{\alpha_s})f(x,\theta)$ exist in a neighbourhood of the true value $\theta_0$ for all $\alpha$ with $\alpha_1+…+\alpha_s\le k+1$ and $E_{\theta_0}|f^{(\alpha)}(X,\theta_0)|^r<\infty$ for some $r>2$. We obtain an expansion of the form
$$ \sqrt{n}(\vartheta_n-\theta_0)=h_1+n^{-1/2}h_2+…+n^{-(k-1)/2}h_k+\zeta_n $$
where the components of $h_j, j=1,\ldots,k$, are polynomials dependent on some random variables of the form $n^{-1/2}\sum\limits_{i=1}^n f^{(\alpha)}(X_i,\theta_0)$ and $\zeta_n$ is a random variable converging to zero at a certain rate.

Full text: PDF file (1216 kB)

English version:
Theory of Probability and its Applications, 1973, 18:2, 295–303

Bibliographic databases:

Received: 06.03.1972

Citation: D. M. Chibisov, “An Asymptotic Expansion for a Class of Estimators Containing Maximum Likelihood Estimators”, Teor. Veroyatnost. i Primenen., 18:2 (1973), 303–311; Theory Probab. Appl., 18:2 (1973), 295–303

Citation in format AMSBIB
\Bibitem{Chi73}
\by D.~M.~Chibisov
\paper An Asymptotic Expansion for a Class of Estimators Containing Maximum Likelihood Estimators
\jour Teor. Veroyatnost. i Primenen.
\yr 1973
\vol 18
\issue 2
\pages 303--311
\mathnet{http://mi.mathnet.ru/tvp4248}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=321227}
\zmath{https://zbmath.org/?q=an:0295.62028}
\transl
\jour Theory Probab. Appl.
\yr 1973
\vol 18
\issue 2
\pages 295--303
\crossref{https://doi.org/10.1137/1118031}


Linking options:
  • http://mi.mathnet.ru/eng/tvp4248
  • http://mi.mathnet.ru/eng/tvp/v18/i2/p303

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. V. Burnashev, “Asymptotic expansions for estimates of a signal parameter in Gaussian white noise”, Math. USSR-Sb., 33:2 (1977), 159–184  mathnet  crossref  mathscinet  zmath  isi
    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. E. E. Zhuk, “Cluster Analysis of the Realizations of Autoregression Time Series”, Autom. Remote Control, 64:1 (2003), 65–75  mathnet  crossref  mathscinet  zmath  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
    Number of views:
    This page:182
    Full text:80

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2021