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

 Teor. Veroyatnost. i Primenen., 1972, Volume 17, Issue 4, Pages 658–668 (Mi tvp4319)

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
$$\mathbf{Z}_n=\mathbf{H}_0(\mathbf{S}_n)+\sum_{j=1}^k n^{-j/2}\mathbf{H}_j(\mathbf{S}_n) \tag{1}$$
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.

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

Bibliographic databases:

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} 

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

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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