Estimation of Distance Correlation: a Simulation-based Comparative Study

Abstract

[Abstract] The notion of distance correlationwas introduced to measure the dependence between two random vectors, not necessarily of equal dimensions, in a multivariate setting. In their work, Sz´ekely et al. (2007) proposed an estimator for the squared distance covariance, and they also proved that this estimator is a V-statistic. On the other hand, Sz´ekely and Rizzo (2014) introduced an unbiased version of the squared sample distance covariance, which was subsequently identified as a U-statistic in Huo and Sz´ekely (2016). In this study, a simulation is conducted to compare both distance correlation estimators: the U-estimator and the V-estimator. The analysis assesses their efficiency (mean squared error) and contrasts the computational times of both approaches across various dependence structures.