Open Access
November 2020 Distance covariance for discretized stochastic processes
Herold Dehling, Muneya Matsui, Thomas Mikosch, Gennady Samorodnitsky, Laleh Tafakori
Bernoulli 26(4): 2758-2789 (November 2020). DOI: 10.3150/20-BEJ1206


Given an i.i.d. sequence of pairs of stochastic processes on the unit interval we construct a measure of independence for the components of the pairs. We define distance covariance and distance correlation based on approximations of the component processes at finitely many discretization points. Assuming that the mesh of the discretization converges to zero as a suitable function of the sample size, we show that the sample distance covariance and correlation converge to limits which are zero if and only if the component processes are independent. To construct a test for independence of the discretized component processes, we show consistency of the bootstrap for the corresponding sample distance covariance/correlation.


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Herold Dehling. Muneya Matsui. Thomas Mikosch. Gennady Samorodnitsky. Laleh Tafakori. "Distance covariance for discretized stochastic processes." Bernoulli 26 (4) 2758 - 2789, November 2020.


Received: 1 October 2018; Revised: 1 December 2019; Published: November 2020
First available in Project Euclid: 27 August 2020

zbMATH: 07256159
MathSciNet: MR4140528
Digital Object Identifier: 10.3150/20-BEJ1206

Keywords: distance covariance , Empirical characteristic function , stochastic process , test of independence

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

Vol.26 • No. 4 • November 2020
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