Asymptotic Behaviour of the Empirical Distance Covariance for Dependent Data

Marius Kroll ()
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Marius Kroll: Ruhr-Universität Bochum

Journal of Theoretical Probability, 2022, vol. 35, issue 2, 1226-1246

Abstract: Abstract We give two asymptotic results for the empirical distance covariance on separable metric spaces without any iid assumption on the samples. In particular, we show the almost sure convergence of the empirical distance covariance for any measure with finite first moments, provided that the samples form a strictly stationary and ergodic process. We further give a result concerning the asymptotic distribution of the empirical distance covariance under the assumption of absolute regularity of the samples and extend these results to certain types of pseudometric spaces. In the process, we derive a general theorem concerning the asymptotic distribution of degenerate V-statistics of order 2 under a strong mixing condition.

Keywords: Distance covariance; Distance correlation; Negative type; Test of independence; Mixing conditions; 62H20; 62G20; 60F05; 30L05 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10959-021-01073-w

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