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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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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DOI: https://doi.org/10.1007/BF01192169
Keywords
- Covariance
- Stochastic Process
- Probability Theory
- Mathematical Biology
- Weak Convergence