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

Axel Bücher ()
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Axel Bücher: Université Catholique de Louvain

Journal of Theoretical Probability, 2015, vol. 28, issue 3, 1028-1037

Abstract: 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 .

Keywords: Multivariate sequential empirical processes; Weak convergence; Strong alpha mixing; Ottaviani’s inequality; 60F17; 60G10; 62G30 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10959-013-0529-5

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