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., 1972, Volume 17, Issue 4, Pages 658–668 (Mi tvp4319)  

This article is cited in 1 scientific paper (total in 1 paper)

An asymptotic expansion for the distribution of a statistic admitting an asymptotic expansion

D. M. Chibisov

Moscow

Abstract: Let $\mathbf{X}_i$, $i=1,…,n$ be $p$-dimensional independent identically distributed random vectors and $\mathbf{S}_n=n^{-1/2}\sum\mathbf{X}_i$. Let $\mathbf{H}_0(\mathbf{x})$ be a linear function from $R^p$ into $R^s$, $s\leq p$, and $\mathbf{H}_j(\mathbf{x})=(H_{j1}(\mathbf{x}),…,H_{js}(\mathbf{x}))$, $j=1,…,k$, where $\mathbf{H}_{jl}(\mathbf{x})$, $\mathbf{x}\in R^p$, $l=1,…,s$, are polinomials. For the distribution of
\begin{equation} \mathbf{Z}_n=\mathbf{H}_0(\mathbf{S}_n)+\sum_{j=1}^k n^{-j/2}\mathbf{H}_j(\mathbf{S}_n) \tag{1} \end{equation}
an asymptotic expansion of the Edgeworth type is obtained. A modification of this result is given for the case when the right hand side of (1) contains a remainder term converging to zero at a certain rate.

Full text: PDF file (1462 kB)

English version:
Theory of Probability and its Applications, 1973, 17:4, 620–630

Bibliographic databases:

Received: 07.10.1971

Citation: D. M. Chibisov, “An asymptotic expansion for the distribution of a statistic admitting an asymptotic expansion”, Teor. Veroyatnost. i Primenen., 17:4 (1972), 658–668; Theory Probab. Appl., 17:4 (1973), 620–630

Citation in format AMSBIB
\Bibitem{Chi72}
\by D.~M.~Chibisov
\paper An asymptotic expansion for the distribution of a statistic admitting an asymptotic expansion
\jour Teor. Veroyatnost. i Primenen.
\yr 1972
\vol 17
\issue 4
\pages 658--668
\mathnet{http://mi.mathnet.ru/tvp4319}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=323007}
\zmath{https://zbmath.org/?q=an:0279.60018}
\transl
\jour Theory Probab. Appl.
\yr 1973
\vol 17
\issue 4
\pages 620--630
\crossref{https://doi.org/10.1137/1117075}


Linking options:
  • http://mi.mathnet.ru/eng/tvp4319
  • http://mi.mathnet.ru/eng/tvp/v17/i4/p658

    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. Zaikin A.A., “Asymptotic Expansion of D-Risks For Hypothesis Testing in Bernoulli Scheme”, Lobachevskii J. Math., 39:3, SI (2018), 413–423  crossref  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
    Number of views:
    This page:136
    Full text:72

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020