Related papers: Copula versions of distance multivariance and dHSI…
We propose a new multivariate dependency measure. It is obtained by considering a Gaussian kernel based distance between the copula transform of the given d-dimensional distribution and the uniform copula and then appropriately normalizing…
Over the last couple of decades, several copula based methods have been proposed in the literature to test for the independence among several random variables. But these existing tests are not invariant under monotone transformations of the…
Distance multivariance is a multivariate dependence measure, which can detect dependencies between an arbitrary number of random vectors each of which can have a distinct dimension. Here we discuss several new aspects, present a concise…
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…
We investigate the problem of testing whether $d$ random variables, which may or may not be continuous, are jointly (or mutually) independent. Our method builds on ideas of the two variable Hilbert-Schmidt independence criterion (HSIC) but…
A new index based on empirical copulas, termed the Copula Statistic (CoS), is introduced for assessing the strength of multivariate dependence and for testing statistical independence. New properties of the copulas are proved. They allow us…
The purpose of this paper is twofold. First, we provide a novel characterization of independence of random vectors based on the checkerboard approximation to a multivariate copula. Using this result, we then propose a new family of tests of…
Following our previous work on copula-based nonsymmetric bivariate dependence measures, we propose a new set of conditions on nonsymmetric multivariate dependence measures which characterize both independence and complete dependence of one…
Following our previous work on copula-based nonsymmetric dependence measures, we introduce similar measures for discrete random variables. The measures cover the range between two extremes: independence and complete dependence, which take…
We propose new statistical tests, in high-dimensional settings, for testing the independence of two random vectors and their conditional independence given a third random vector. The key idea is simple, i.e., we first transform each…
In this article, we study tests of independence for data with arbitrary distributions in the non-serial case, i.e., for independent and identically distributed random vectors, as well as in the serial case, i.e., for time series. These…
This paper proposes some novel one-sided omnibus tests for independence between two multivariate stationary time series. These new tests apply the Hilbert-Schmidt independence criterion (HSIC) to test the independence between the…
Dependence measures based on reproducing kernel Hilbert spaces, also known as Hilbert-Schmidt Independence Criterion and denoted HSIC, are widely used to statistically decide whether or not two random vectors are dependent. Recently,…
Testing for pairwise independence for the case where the number of variables may be of the same size or even larger than the sample size has received increasing attention in the recent years. We contribute to this branch of the literature…
The paper presents a new copula based method for measuring dependence between random variables. Our approach extends the Maximum Mean Discrepancy to the copula of the joint distribution. We prove that this approach has several advantageous…
Identification of joint dependence among more than two random vectors plays an important role in many statistical applications, where the data may contain sensitive or confidential information. In this paper, we consider the the…
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,…
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 Hilbert--Schmidt Independence Criterion (HSIC) is a popular measure of the dependency between two random variables. The statistic dHSIC is an extension of HSIC that can be used to test joint independence of $d$ random variables. Such…
Many tools exist to detect dependence between random variables, a core question across a wide range of machine learning, statistical, and scientific endeavors. Although several statistical tests guarantee eventual detection of any…