RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 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

 Teor. Veroyatnost. i Primenen., 2008, Volume 53, Issue 2, Pages 390–393 (Mi tvp2422)

Short Communications

Nonclassical Error Bounds for Asymptotic Expansions in the Central Limit Theorem

L. S. Yaroslavtseva

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: We present the first nonclassical error bound for short asymptotic expansions in the central limit theorem in $R$ for the case of independent but not necessarily identically distributed random variables. In the case of independent identically distributed random variables under the Cramér condition, this bound provides the correct order of convergence $(1/n)$, and the leading term in the bound is determined by powers of the third and fourth pseudomoments of the random summands.

Keywords: nonclassical error bound, pseudomoment, asymptotic expansions, central limit theorem.

DOI: https://doi.org/10.4213/tvp2422

Full text: PDF file (507 kB)
References: PDF file   HTML file

English version:
Theory of Probability and its Applications, 2009, 53:2, 365–367

Bibliographic databases:

Citation: L. S. Yaroslavtseva, “Nonclassical Error Bounds for Asymptotic Expansions in the Central Limit Theorem”, Teor. Veroyatnost. i Primenen., 53:2 (2008), 390–393; Theory Probab. Appl., 53:2 (2009), 365–367

Citation in format AMSBIB
\Bibitem{Yar08} \by L.~S.~Yaroslavtseva \paper Nonclassical Error Bounds for Asymptotic Expansions in the Central Limit Theorem \jour Teor. Veroyatnost. i Primenen. \yr 2008 \vol 53 \issue 2 \pages 390--393 \mathnet{http://mi.mathnet.ru/tvp2422} \crossref{https://doi.org/10.4213/tvp2422} \zmath{https://zbmath.org/?q=an:1191.60031} \transl \jour Theory Probab. Appl. \yr 2009 \vol 53 \issue 2 \pages 365--367 \crossref{https://doi.org/10.1137/S0040585X97983699} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000267617600017} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-67249103668} 

• http://mi.mathnet.ru/eng/tvp2422
• https://doi.org/10.4213/tvp2422
• http://mi.mathnet.ru/eng/tvp/v53/i2/p390

 SHARE:

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. A. V. Syulyukin, “On asymptotic expansions for convolutions of distributions belonging to the domains of attraction of stable laws”, Theory Probab. Appl., 58:3 (2014), 518–524
•  Number of views: This page: 129 Full text: 25 References: 25