Distance covariance for discretized stochastic processes

Publikation: Bidrag til tidsskriftTidsskriftartikelfagfællebedømt

Dokumenter

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.
OriginalsprogEngelsk
TidsskriftBernoulli
Vol/bind26
Sider (fra-til)2758-2789
ISSN1350-7265
DOI
StatusUdgivet - 2020

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