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Teoriya Veroyatnostei i ee Primeneniya, 1996, Volume 41, Issue 3, Pages 533–560
DOI: https://doi.org/10.4213/tvp3134 (Mi tvp3134) 		 
This article is cited in 18 scientific papers (total in 18 papers)

On the distribution of the ratio of sums of random variables

S. Yu. Novak

Siberian State Academy of Geodesy
Full-text PDF (1107 kB) Citations (18)
DOI: https://doi.org/10.4213/tvp3134
Abstract: We study the distribution of the ratio $Z_n$ of sums of random variables. Berry–Esseen-type estimates of the rate of convergence in the central limit theorem for $Z_n$ are given. In addition, second-order asymptotic expansions for $\mathbb E Z_n$ and $\mathbb E Z^2_n$ are presented.
The results are applied to the problems of nonparametric regression curve estimation, nonparametric tail index estimation, and nonparametric estimation of a hazard function.
Keywords: Berry–Esseen-type estimates, regression, tail index, hazard function, mean square error.
Received: 26.08.1993
English version:
Theory of Probability and its Applications, 1997, Volume 41, Issue 3, Pages 479–503
DOI: https://doi.org/10.1137/S0040585X97975228
Bibliographic databases:
Language: Russian
Citation: S. Yu. Novak, “On the distribution of the ratio of sums of random variables”, Teor. Veroyatnost. i Primenen., 41:3 (1996), 533–560; Theory Probab. Appl., 41:3 (1997), 479–503
Citation in format AMSBIB
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\by S.~Yu.~Novak
\paper On the distribution of the ratio of sums of random variables
\jour Teor. Veroyatnost. i Primenen.
\yr 1996
\vol 41
\issue 3
\pages 533--560
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\transl
\jour Theory Probab. Appl.
\yr 1997
\vol 41
\issue 3
\pages 479--503
\crossref{https://doi.org/10.1137/S0040585X97975228}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1997XZ71800006}
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  • https://www.mathnet.ru/eng/tvp/v41/i3/p533
    • This publication is cited in the following 18 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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