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A Glivenko-Cantelli lemma and weak convergence for empirical processes of associated sequences
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  • Published: September 1993

A Glivenko-Cantelli lemma and weak convergence for empirical processes of associated sequences

  • Hao Yu1 

Probability Theory and Related Fields volume 95, pages 357–370 (1993)Cite this article

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Summary

With the help of an extension of Hoeffding's equality, we develop a way for estimating the covariance structures for empirical functions of associated sequences in terms of covariances of the original random variables. Based on these estimations, a Glivenko-Cantelli lemma for associated sequences and weak convergence for empirical processes of stationary associated sequences are obtained, all under the conditions on covariances of the original random variables.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Carleton University, K1S 5B6, Ottawa, Canada

    Hao Yu

Authors
  1. Hao Yu
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Additional information

This research has been supported partially by a scholarship from the Faculty of Graduate Studies and Research of Carleton University, Ottawa, and by an NSERC Canada grant of M. Csörgő

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Yu, H. A Glivenko-Cantelli lemma and weak convergence for empirical processes of associated sequences. Probab. Th. Rel. Fields 95, 357–370 (1993). https://doi.org/10.1007/BF01192169

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  • Received: 25 October 1991

  • Revised: 21 September 1992

  • Issue Date: September 1993

  • DOI: https://doi.org/10.1007/BF01192169

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Keywords

  • Covariance
  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Weak Convergence
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