Related papers: Fast Computing for Distance Covariance
Classical dependence measures such as Pearson correlation, Spearman's $\rho$, and Kendall's $\tau$ can detect only monotonic or linear dependence. To overcome these limitations, Szekely et al.(2007) proposed distance covariance as a…
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…
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 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…
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…
Distance covariance is a widely used statistical methodology for testing the dependency between two groups of variables. Despite the appealing properties of consistency and superior testing power, the testing results of distance covariance…
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…
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,…
Distance covariance and distance correlation are scalar coefficients that characterize independence of random vectors in arbitrary dimension. Properties, extensions, and applications of distance correlation have been discussed in the recent…
(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…
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…
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…
In machine learning and particularly in topological data analysis, $\epsilon$-graphs are important tools but are generally hard to compute as the distance calculation between n points takes time O(n^2) classically. Recently, quantum…
Cooperative localization is a promising solution to improve the accuracy and overcome the shortcomings of GNSS. Cooperation is often achieved by measuring the distance between users. To optimally integrate a distance measurement between two…
This paper introduces a new way to calculate distance-based statistics, particularly when the data are multivariate. The main idea is to pre-calculate the optimal projection directions given the variable dimension, and to project…
Variable selection is of increasing importance to address the difficulties of high dimensionality in many scientific areas. In this paper, we demonstrate a property for distance covariance, which is incorporated in a novel feature screening…
Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to…
We consider the problem of calculating distance correlation coefficients between random vectors whose joint distributions belong to the class of Lancaster distributions. We derive under mild convergence conditions a general series…
Correlation filters take advantage of specific properties in the Fourier domain allowing them to be estimated efficiently: O(NDlogD) in the frequency domain, versus O(D^3 + ND^2) spatially where D is signal length, and N is the number of…