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Distance covariance for discretized stochastic processes

Author
Dehling, Harold; Matsui, Muneya; Mikosch, Thomas; Samorodnitsky, Gennady; Tafakori, Laleh
Abstract
Given an iid 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.
Sponsorship
Herold Dehling's research was partially supported by the DFG through the
Collaborative Research Grant SFB 823. Muneya Matsui's research is partly supported by the JSPS Grant-in-Aid
for Young Scientists B (16k16023).
Thomas Mikosch's research was partly supported by an Alexander von Humboldt
Research Award. Gennady Samorodnitsky's research was partially supported by the ARO
grant W911NF-12-10385 at Cornell University. Laleh Tafakori would like to thank the Australian Research Council for support through Laureate Fellowship FL130100039.
Date Issued
2018-06-26Subject
distance covariance; empirical characteristic function; test for independence; stochastic processes
Type
article