Estimation of distance correlation: a simulation-based comparative study

Ponente(s): Blanca Estela Monroy Castillo, María Amalia Jácome Pumar and Ricardo Cao Abad

Distance correlation is a new class of multivariate dependence coefficients applicable to random vectors of arbitrary and not necessarily equal dimension. Even more, distance correlation, unlike the Pearson's correlation coefficient, is zero only if the random vectors are independent. Since its introduction, distance correlation has had many applications in, for example, life science, variable selection and has been extended to different contexts. In 2014 an unbiased version of the squared sample distance covariance is proposed. Then, in 2016 is proved that the unbiased estimator turns out to be a U-statistic. In this work, a simulation study is developed to compare the estimations of distance correlation by means of the estimation proposed by V-statistics and the estimation through U-statistics. The study shows the efficiency (MSE) and compares the computational time for both methods under different dependence structures.