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Teor. Veroyatnost. i Primenen., 1998, Volume 43, Issue 1, Pages 69–81 (Mi tvp824)  

This article is cited in 2 scientific papers (total in 2 papers)

Estimates of the convergence ratein the central limit theorem for generalized $U$-statistics

Sh. A. Khashimov, G. R. Abdurakhmanov

Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan

Abstract: Estimates are found of the convergence rate in the central limit theorem for generalized nondegenerate $U$-statistics. The estimates obtained refine and generalize a number of known results in this field.

Keywords: generalized $U$-statistics, characteristic function, normal distribution.

DOI: https://doi.org/10.4213/tvp824

Full text: PDF file (541 kB)

English version:
Theory of Probability and its Applications, 1999, 43:1, 63–74

Bibliographic databases:

Received: 21.05.1996

Citation: Sh. A. Khashimov, G. R. Abdurakhmanov, “Estimates of the convergence ratein the central limit theorem for generalized $U$-statistics”, Teor. Veroyatnost. i Primenen., 43:1 (1998), 69–81; Theory Probab. Appl., 43:1 (1999), 63–74

Citation in format AMSBIB
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\by Sh.~A.~Khashimov, G.~R.~Abdurakhmanov
\paper Estimates of the convergence ratein the central limit theorem for generalized $U$-statistics
\jour Teor. Veroyatnost. i Primenen.
\yr 1998
\vol 43
\issue 1
\pages 69--81
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\zmath{https://zbmath.org/?q=an:0958.60022}
\transl
\jour Theory Probab. Appl.
\yr 1999
\vol 43
\issue 1
\pages 63--74
\crossref{https://doi.org/10.1137/S0040585X97976660}
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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. L. V. Gadasina, “A Berry–Esseen bound for $U$-statistics”, J. Math. Sci. (N. Y.), 128:1 (2005), 2522–2537  mathnet  crossref  mathscinet  zmath
    2. L. V. Gadasina, “Berry–Esseen inequalities for $U$-statistics”, Theory Probab. Appl., 48:1 (2004), 147–152  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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