Related papers: A novel characterization and new simple tests of m…
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…
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…
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…
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…
Continuation refers to the operation by which the cumulative distribution function of a discontinuous random vector is made continuous through multilinear interpolation. The copula that results from the application of this technique to the…
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…
Copulas are mathematical objects that fully capture the dependence structure among random variables and hence, offer a great flexibility in building multivariate stochastic models. In statistics, a copula is used as a general way of…
We study the problem of choosing the copula when the marginal distributions of a random vector are not all continuous. Inspired by four motivating examples including simulation from copulas, stress scenarios, co-risk measures, and…
The multivariate Hilbert-Schmidt-Independence-Criterion (dHSIC) and distance multivariance allow to measure and test independence of an arbitrary number of random vectors with arbitrary dimensions. Here we define versions which only depend…
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…
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…
Working with so-called linkages allows to define a copula-based, $[0,1]$-valued multivariate dependence measure $\zeta^1(\boldsymbol{X},Y)$ quantifying the scale-invariant extent of dependence of a random variable $Y$ on a $d$-dimensional…
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…
This article proposes copula-based dependence quantification between multiple groups of random variables of possibly different sizes via the family of $Phi$-divergences. An axiomatic framework for this purpose is provided, after which we…
We introduce a new test procedure of independence in the framework of parametric copulas with unknown marginals. The method is based essentially on the dual representation of $\chi^2$-divergence on signed finite measures. The asymptotic…
Simple correlation coefficients between two variables have been generalized to measure association between two matrices in many ways. Coefficients such as the RV coefficient, the distance covariance (dCov) coefficient and kernel based…
Testing independence among a number of (ultra) high-dimensional random samples is a fundamental and challenging problem. By arranging $n$ identically distributed $p$-dimensional random vectors into a $p \times n$ data matrix, we investigate…
Copulas have now become ubiquitous statistical tools for describing, analysing and modelling dependence between random variables. Sklar's theorem, "the fundamental theorem of copulas", makes a clear distinction between the continuous case…
A framework for quantifying dependence between random vectors is introduced. With the notion of a collapsing function, random vectors are summarized by single random variables, called collapsed random variables in the framework. Using this…
Multivariate datasets are common in various real-world applications. Recently, copulas have received significant attention for modeling dependencies among random variables. A copula-based information measure is required to quantify the…