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Teor. Veroyatnost. i Primenen., 1980, Volume 25, Issue 4, Pages 745–756 (Mi tvp1229)  

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

Asymptotic expansion for the distribution of a statistic admitting a stochastic expansion. I

D. M. Čibisov

Moscow

Abstract: Let $(Y_{0i},\mathbf Y_i)=(Y_{0i},Y_{1i},…,Y_{pi})$, $i=1,…,n$, be i.i.d. random vectors in $R^{p+1}$, and $\{h_j\}$ be a finite set of polinomials of $p+1$ variables. Let
\begin{gather*} S_n=n^{-1/2}\sum Y_{0i},\qquad T_{nl}=n^{-1/2}\sum Y_{li},\qquad\mathbf T_n=(T_{n1},…,T_{np}),
Z_n=S_n+\sum n^{-j/2}h_j(S_n,\mathbf T_n). \end{gather*}
In the paper an asymptotic expansion of the Edgeworth's type for the distribution function of $Z_n$ is obtained under conditions which are weaker than those previously known.

Full text: PDF file (665 kB)

English version:
Theory of Probability and its Applications, 1981, 25:4, 732–744

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Received: 21.09.1978

Citation: D. M. Čibisov, “Asymptotic expansion for the distribution of a statistic admitting a stochastic expansion. I”, Teor. Veroyatnost. i Primenen., 25:4 (1980), 745–756; Theory Probab. Appl., 25:4 (1981), 732–744

Citation in format AMSBIB
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\by D.~M.~{\v C}ibisov
\paper Asymptotic expansion for the distribution of a~statistic admitting a~stochastic expansion.~I
\jour Teor. Veroyatnost. i Primenen.
\yr 1980
\vol 25
\issue 4
\pages 745--756
\mathnet{http://mi.mathnet.ru/tvp1229}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=595136}
\zmath{https://zbmath.org/?q=an:0482.62009|0464.62017}
\transl
\jour Theory Probab. Appl.
\yr 1981
\vol 25
\issue 4
\pages 732--744
\crossref{https://doi.org/10.1137/1125088}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1980MK50200006}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. Yu. Novak, “On self-normalized sums and Student's statistic”, Theory Probab. Appl., 49:2 (2005), 336–344  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Hall P., Wang Q.Y., “Exact convergence rate and leading term in central limit theorem for student's t statistic”, Annals of Probability, 32:2 (2004), 1419–1437  crossref  mathscinet  zmath  isi
    3. Wang Q., Hall P., “Relative Errors in Central Limit Theorems for Student's T Statistic, with Applications”, Statistica Sinica, 19:1 (2009), 343–354  mathscinet  zmath  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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