Distance covariance for discretized stochastic processes
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Distance covariance for discretized stochastic processes. / Dehling, Herold G.; Matsui, Muneya ; Mikosch, Thomas Valentin; Samorodnitsky, Gennady; Tafakori, Laleh .
In: Bernoulli, Vol. 26, 2020, p. 2758-2789.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Distance covariance for discretized stochastic processes
AU - Dehling, Herold G.
AU - Matsui, Muneya
AU - Mikosch, Thomas Valentin
AU - Samorodnitsky, Gennady
AU - Tafakori, Laleh
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
U2 - 10.3150/20-BEJ1206
DO - 10.3150/20-BEJ1206
M3 - Journal article
VL - 26
SP - 2758
EP - 2789
JO - Bernoulli
JF - Bernoulli
SN - 1350-7265
ER -
ID: 248031539