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On Edgeworth expansions for dependency-neighborhoods chain structures and Stein's method
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  • Published: 12 May 2003

On Edgeworth expansions for dependency-neighborhoods chain structures and Stein's method

  • Yosef Rinott1,2 &
  • Vladimir Rotar3,4 

Probability Theory and Related Fields volume 126, pages 528–570 (2003)Cite this article

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  • 9 Citations

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Abstract

Let W be the sum of dependent random variables, and h(x) be a function. This paper provides an Edgeworth expansion of an arbitrary ``length'' for %E{h(W)} in terms of certain characteristics of dependency, and of the smoothness of h and/or the distribution of W. The core of the class of dependency structures for which these characteristics are meaningful is the local dependency, but in fact, the class is essentially wider. The remainder is estimated in terms of Lyapunov's ratios. The proof is based on a Stein's method.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of California, San Diego, USA

    Yosef Rinott

  2. Department of Statistics, Hebrew University, Israel

    Yosef Rinott

  3. Department of Mathematics, San Diego State University, San Diego, USA

    Vladimir Rotar

  4. the Central Economics and Mathematics, Institute of Russian Academy of Sciences, Russia

    Vladimir Rotar

Authors
  1. Yosef Rinott
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  2. Vladimir Rotar
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Corresponding author

Correspondence to Yosef Rinott.

Additional information

Supported in part by NSF grant DMS-98-03623

Supported in part by the Russian Foundation of Basic Research, grant # 00-01-00194, and by NSF grant DMS-98-03623

Mathematics Subject Classification (2000):Primary 62E20; Secondary 60E05

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Rinott, Y., Rotar, V. On Edgeworth expansions for dependency-neighborhoods chain structures and Stein's method. Probab. Theory Relat. Fields 126, 528–570 (2003). https://doi.org/10.1007/s00440-003-0271-5

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  • Received: 28 October 2000

  • Revised: 26 February 2003

  • Published: 12 May 2003

  • Issue Date: August 2003

  • DOI: https://doi.org/10.1007/s00440-003-0271-5

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Keywords

  • Edgeworth expansion
  • Local dependency
  • Stein's method
  • Non-complete U-statistics
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