Distance covariance for discretized stochastic processes

dc.contributor.authorDehling, Harold
dc.contributor.authorMatsui, Muneya
dc.contributor.authorMikosch, Thomas
dc.contributor.authorSamorodnitsky, Gennady
dc.contributor.authorTafakori, Laleh
dc.description.abstractGiven 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.en_US
dc.description.sponsorshipHerold 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.en_US
dc.subjectdistance covarianceen_US
dc.subjectempirical characteristic functionen_US
dc.subjecttest for independenceen_US
dc.subjectstochastic processesen_US
dc.titleDistance covariance for discretized stochastic processesen_US


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