Testing for independence in high dimensions based on empirical copulas
The Annals of Statistics · 2024 · Volume 52 · Issue 1
Abstract
Testing for pairwise independence for the case where the number of variables may be of the same size or even larger than the sample size has received increasing attention in the recent years. We contribute to this branch of the literature by considering tests that allow to detect higher-order dependencies. The proposed methods are based on connecting the problem to copulas and making use of the Moebius transformation of the empirical copula process; an approach that is related to Lancaster interactions and that has already been used successfully for the case where the number of variables is fixed. Based on a martingale central limit theorem, it is shown that respective test statistics converge to the standard normal distribution, allowing for straightforward definition of critical values. The results are illustrated by a Monte Carlo simulation study.
Keywords
60F05, 62G10, 62H15, empirical copula process, High-dimensional statistics, higher-order dependence, Lancaster interaction, Moebius transform, rank based inference
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