Related papers: A fast algorithm for computing distance correlatio…
Distance covariance and distance correlation have been widely adopted in measuring dependence of a pair of random variables or random vectors. If the computation of distance covariance and distance correlation is implemented directly…
Distance correlation is a novel class of multivariate dependence measure, taking positive values between 0 and 1, and applicable to random vectors of arbitrary dimensions, not necessarily equal. It offers several advantages over the…
In this paper, we propose a novel Euclidean-distance-based coefficient, named differential distance correlation, to measure the strength of dependence between a random variable $ Y \in \mathbb{R} $ and a random vector $ \boldsymbol{X} \in…
Testing the independence between random vectors is a fundamental problem in statistics. Distance correlation, a recently popular dependence measure, is universally consistent for testing independence against all distributions with finite…
Test of independence plays a fundamental role in many statistical techniques. Among the nonparametric approaches, the distance-based methods (such as the distance correlation based hypotheses testing for independence) have numerous…
The distance covariance of two random vectors is a measure of their dependence. The empirical distance covariance and correlation can be used as statistical tools for testing whether two random vectors are independent. We propose an analogs…
Distance correlation is a new measure of dependence between random vectors. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but unlike the classical definition of correlation,…
(To appear in The American Statistician.) Distance covariance (Sz\'ekely, Rizzo, and Bakirov, 2007) is a fascinating recent notion, which is popular as a test for dependence of any type between random variables $X$ and $Y$. This approach…
Distance covariance is a quantity to measure the dependence of two random vectors. We show that the original concept introduced and developed by Sz\'{e}kely, Rizzo and Bakirov can be embedded into a more general framework based on symmetric…
Many statistical applications require the quantification of joint dependence among more than two random vectors. In this work, we generalize the notion of distance covariance to quantify joint dependence among d >= 2 random vectors. We…
Distance correlation is a measure of dependence between two paired random vectors or matrices of arbitrary, not necessarily equal, dimensions. Unlike Pearson correlation, the population distance correlation coefficient is zero if and only…
The distance covariance of Sz\'ekely, et al. [23] and Sz\'ekely and Rizzo [21], a powerful measure of dependence between sets of multivariate random variables, has the crucial feature that it equals zero if and only if the sets are mutually…
The concept of distance covariance/correlation was introduced recently to characterize dependence among vectors of random variables. We review some statistical aspects of distance covariance/correlation function and we demonstrate its…
We introduce two new measures for the dependence of $n \ge 2$ random variables: distance multivariance and total distance multivariance. Both measures are based on the weighted $L^2$-distance of quantities related to the characteristic…
Identifying independence between two random variables or correlated given their samples has been a fundamental problem in Statistics. However, how to do so in a space-efficient way if the number of states is large is not quite well-studied.…
In this paper, we introduce a ${\mathcal L}_2$ type test for testing mutual independence and banded dependence structure for high dimensional data. The test is constructed based on the pairwise distance covariance and it accounts for the…
Distance covariance is a popular measure of dependence between random variables. It has some robustness properties, but not all. We prove that the influence function of the usual distance covariance is bounded, but that its breakdown value…
In this paper, we study distance covariance, Hilbert-Schmidt covariance (aka Hilbert-Schmidt independence criterion [Gretton et al. (2008)]) and related independence tests under the high dimensional scenario. We show that the sample…
Given an iid sequence of pairs of stochastic processes on the unit interval we construct a measure of independence for the components of the pairs. We define distance covariance and distance correlation based on approximations of the…
We propose three measures of mutual dependence between multiple random vectors. All the measures are zero if and only if the random vectors are mutually independent. The first measure generalizes distance covariance from pairwise dependence…