B1980
Title: Improved distance correlation estimation
Authors: Blanca Monroy-Castillo - Universidade da Coruna (Spain) [presenting]
Maria Amalia Jacome Pumar - Universidade da Coruna (Spain)
Ricardo Cao - Universidade da Coruna (Spain)
Abstract: Distance correlation is a novel class of multivariate dependence coefficients applicable to random vectors of arbitrary dimensions, not necessarily equal. It offers several advantages over the well-known Pearson correlation coefficient. One of the most important advantages is that distance correlation equals zero if and only if the random vectors are independent. Since its introduction, distance correlation has found numerous applications in different fields. There are two different estimators of the distance correlation available in the literature. The first one is based on an asymptotically unbiased estimator of the distance covariance, which turns out to be a V-statistic. The second one builds on an unbiased estimator of the distance covariance, which is a U-statistic. A simulation is conducted to compare both distance correlation estimators. The study evaluates their efficiency (mean squared error) and compares computational times for both methods under different dependence structures. To tackle the challenge of selecting the best estimator, a potential solution given by a convex linear combination of the former estimators is proposed and studied.
