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A Note on Weak Convergence of the Sequential Multivariate Empirical Process Under Strong Mixing

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Abstract

This article investigates weak convergence of the sequential \(d\)-dimensional empirical process under strong mixing. Weak convergence is established for mixing rates \(\alpha _n = O(n^{-a})\), where \(a>1\), which slightly improves upon existing results in the literature that are based on mixing rates depending on the dimension \(d\).

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Acknowledgments

The author would like to thank two anonymous referees and an Associate Editor for their constructive comments on an earlier version of this manuscript, which led to a substantial improvement of the paper. The author is also thankful to Ivan Kojadinovic for thorough proofreading and numerous suggestions concerning this manuscript. This work has been supported in parts by the Collaborative Research Center “Statistical modeling of nonlinear dynamic processes” (SFB 823) of the German Research Foundation (DFG) and by the IAP research network Grant P7/06 of the Belgian government (Belgian Science Policy), which is gratefully acknowledged.

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  1. Institut de Statistique, Université Catholique de Louvain, Voie du Roman Pays 20, 1348 , Louvain-la-Neuve, Belgium

    Axel Bücher

  2. Fakultät für Mathematik, Ruhr-Universität Bochum, Universitätsstraße 150, 44780 Bochum, Germany

    Axel Bücher

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  1. Axel Bücher
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Bücher, A. A Note on Weak Convergence of the Sequential Multivariate Empirical Process Under Strong Mixing. J Theor Probab 28, 1028–1037 (2015). https://doi.org/10.1007/s10959-013-0529-5

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  • DOI: https://doi.org/10.1007/s10959-013-0529-5

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