Block Bootstrapping the Empirical Distance Covariance

12/28/2021

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We prove the validity of a non-overlapping block bootstrap for the empirical distance covariance under the assumption of strictly stationary and absolutely regular sample data. From this, we develop a test for independence of two strictly stationary and absolutely regular processes. In proving our results, we derive explicit bounds on the expected Wasserstein distance between an empirical measure and its limit for strictly stationary and strongly mixing sample sequences.

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Block Bootstrapping the Empirical Distance Covariance

Convergence of the empirical two-sample U-statistics with β-mixing data

Convergence of the empirical measure in expected Wasserstein distance: non asymptotic explicit bounds in ℝ^d

Distance covariance for discretized stochastic processes

Asymptotic Behaviour of the Empirical Distance Covariance for Dependent Data

Wasserstein distance bounds on the normal approximation of empirical autocovariances and cross-covariances under non-stationarity and stationarity

Some notes on ergodic theorem for U-statistics of order m for stationary and not necessarily ergodic sequences

On the behavior of the DFA and DCCA in trend-stationary processes

Block Bootstrapping the Empirical Distance Covariance

Related Research

Convergence of the empirical two-sample U-statistics with β-mixing data

Convergence of the empirical measure in expected Wasserstein distance: non asymptotic explicit bounds in ℝ^d

Distance covariance for discretized stochastic processes

Asymptotic Behaviour of the Empirical Distance Covariance for Dependent Data

Wasserstein distance bounds on the normal approximation of empirical autocovariances and cross-covariances under non-stationarity and stationarity

Some notes on ergodic theorem for U-statistics of order m for stationary and not necessarily ergodic sequences

On the behavior of the DFA and DCCA in trend-stationary processes