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

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  • Axel Bücher

    (Université Catholique de Louvain
    Ruhr-Universität Bochum)

Abstract

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

Suggested Citation

  • Axel Bücher, 2015. "A Note on Weak Convergence of the Sequential Multivariate Empirical Process Under Strong Mixing," Journal of Theoretical Probability, Springer, vol. 28(3), pages 1028-1037, September.
    • Handle: RePEc:spr:jotpro:v:28:y:2015:i:3:d:10.1007_s10959-013-0529-5
    DOI: 10.1007/s10959-013-0529-5
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    References listed on IDEAS

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    1. Inoue, Atsushi, 2001. "Testing For Distributional Change In Time Series," Econometric Theory, Cambridge University Press, vol. 17(1), pages 156-187, February.
    2. Xiaofeng Shao, 2010. "A self‐normalized approach to confidence interval construction in time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 343-366, June.
    3. Paul Doukhan & Jean-David Fermanian & Gabriel Lang, 2009. "An empirical central limit theorem with applications to copulas under weak dependence," Statistical Inference for Stochastic Processes, Springer, vol. 12(1), pages 65-87, February.
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