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Teoriya Veroyatnostei i ee Primeneniya, 1966, Volume 11, Issue 3, Pages 369–380 (Mi tvp637)  

This article is cited in 32 scientific papers (total in 32 papers)

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

S. M. Sadikova

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.
Received: 25.05.1966
English version:
Theory of Probability and its Applications, 1966, Volume 11, Issue 3, Pages 325–335
DOI: https://doi.org/10.1137/1111035
Bibliographic databases:
Language: Russian
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://mathscinet.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}
Linking options:
  • https://www.mathnet.ru/eng/tvp637
  • https://www.mathnet.ru/eng/tvp/v11/i3/p369
    Erratum
    This publication is cited in the following 32 articles:
    1. Theory Probab. Appl., 67:3 (2022), 452–464  mathnet  crossref  crossref  mathscinet
    2. N. G. Gamkrelidze, “Issledovaniya po reshetchatym raspredeleniyam teorii veroyatnostei”, Issledovaniya po reshetchatym raspredeleniyam teorii veroyatnostei, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 218, VINITI RAN, M., 2022, 3–66  mathnet  crossref  mathscinet
    3. Maximilian Coblenz, Oliver Grothe, Klaus Herrmann, Marius Hofert, “Smooth bootstrapping of copula functionals”, Electron. J. Statist., 16:1 (2022)  crossref
    4. Mangerel A.P., “On the Bivariate Erds-Kac Theorem and Correlations of the Mobius Function”, Math. Proc. Camb. Philos. Soc., 169:3 (2020), 547–605  crossref  isi
    5. Liwang Ding, Ping Chen, Li Yongming, “On some inequalities for ψ-mixing sequences and its applications in conditional value-at-risk estimate”, Communications in Statistics - Theory and Methods, 49:22 (2020), 5455  crossref
    6. ADAM J. HARPER, “MOMENTS OF RANDOM MULTIPLICATIVE FUNCTIONS, I: LOW MOMENTS, BETTER THAN SQUAREROOT CANCELLATION, AND CRITICAL MULTIPLICATIVE CHAOS”, Forum of Mathematics, Pi, 8 (2020)  crossref
    7. 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  mathnet  crossref  crossref  mathscinet  isi  elib
    8. T. Çağin, P. E. Oliveira, “A Note on Weighted Sums of Associated Random Variables”, Acta Math. Hungar., 143:1 (2014), 96  crossref
    9. Yongming Li, Shanchao Yang, Chengdong Wei, “Some inequalities for strong mixing random variables with applications to density estimation”, Statistics & Probability Letters, 81:2 (2011), 250  crossref
    10. J. Wolf, “The structure of popular difference sets”, Isr. J. Math., 179:1 (2010), 253  crossref
    11. Paulauskas V., “On the rate of convergence to bivariate stable laws”, Lithuanian Mathematical Journal, 49:4 (2009), 426–445  crossref  mathscinet  zmath  isi
    12. Wan-Ying Chang, Donald St.P. Richards, “Finite-sample inference with monotone incomplete multivariate normal data, I”, Journal of Multivariate Analysis, 100:9 (2009), 1883  crossref
    13. Henriques C., Oliveira P.E., “Large deviations for the empirical mean of associated random variables”, Statistics & Probability Letters, 78:6 (2008), 594–598  crossref  mathscinet  zmath  isi
    14. Carla Henriques, Paulo Eduardo Oliveira, “Strong convergence rates for the estimation of a covariance operator for associated samples”, Stat Infer Stoch Process, 11:1 (2007), 77  crossref
    15. 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  crossref  mathscinet  zmath  isi
    16. 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  crossref  mathscinet  zmath  isi
    17. Zhengyan Lin, “ASYMPTOTIC NORMALITY OF KERNEL ESTIMATES OF A DENSITY FUNCTION UNDER ASSOCIATION DEPENDENCE”, Acta Mathematica Scientia, 23:3 (2003), 345  crossref
    18. B.L.S. Prakasa Rao, “Another Esseen-type inequality for multivariate probability density functions”, Statistics & Probability Letters, 60:2 (2002), 191  crossref
    19. George G. Roussas, “An Esseen-type inequality for probability density functions, with an application”, Statistics & Probability Letters, 51:4 (2001), 397  crossref
    20. B.L.S. Prakasa Rao, Isha Dewan, Handbook of Statistics, 19, Stochastic Processes: Theory and Methods, 2001, 693  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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    Теория вероятностей и ее применения Theory of Probability and its Applications
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