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

 Teor. Veroyatnost. i Primenen., 1966, Volume 11, Issue 3, Pages 369–380 (Mi tvp637)

On two-dimensional analogs of an inequality of K. G. Esseen and their application to the Central Limit Theorem

Moscow Engineering Physics Institute

Abstract: A generalization of the well-known inequality of K. G. Esseen [1] for two-dimensional case as well as some estimates of the difference $P(A)-Q(A)$ in terms of characteristic functions are given.

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English version:
Theory of Probability and its Applications, 1966, 11:3, 325–335

Bibliographic databases:

Citation: S. M. Sadikova, “On two-dimensional analogs of an inequality of K. G. Esseen and their application to the Central Limit Theorem”, Teor. Veroyatnost. i Primenen., 11:3 (1966), 369–380; Theory Probab. Appl., 11:3 (1966), 325–335

Citation in format AMSBIB
\Bibitem{Sad66} \by S.~M.~Sadikova \paper On two-dimensional analogs of an inequality of K.\,G.~Esseen and their application to the Central Limit Theorem \jour Teor. Veroyatnost. i Primenen. \yr 1966 \vol 11 \issue 3 \pages 369--380 \mathnet{http://mi.mathnet.ru/tvp637} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=207016} \zmath{https://zbmath.org/?q=an:0202.48503} \transl \jour Theory Probab. Appl. \yr 1966 \vol 11 \issue 3 \pages 325--335 \crossref{https://doi.org/10.1137/1111035} 

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Erratum

This publication is cited in the following articles:
1. Henriques C., Oliveira P.E., “Estimation of a two–dimensional distribution function under association”, Journal of Statistical Planning and Inference, 113:1 (2003), 137–150
2. Henriques C., Oliveira P.E., “Convergence rates for the estimation of two–dimensional distribution functions under association and estimation of the covariance of the limit empirical process”, Journal of Nonparametric Statistics, 18:2 (2006), 119–128
3. Henriques C., Oliveira P.E., “Large deviations for the empirical mean of associated random variables”, Statistics & Probability Letters, 78:6 (2008), 594–598
4. Paulauskas V., “On the rate of convergence to bivariate stable laws”, Lithuanian Mathematical Journal, 49:4 (2009), 426–445
5. D. V. Belomestny, A. V. Prokhorov, “Stability of characterization the independence of random variables by the independence of the linear statistics”, Theory Probab. Appl., 59:4 (2015), 672–677
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