Related papers: A consistent multivariate test of association base…
In this article, we study the test for independence of two random elements $X$ and $Y$ lying in an infinite dimensional space ${\cal{H}}$ (specifically, a real separable Hilbert space equipped with the inner product $\langle .,…
This paper proposes a nonparametric test of pairwise independence of one random variable from a large pool of other random variables. The test statistic is the maximum of several Chatterjee's rank correlations and critical values are…
The problem of detecting changes in covariance for a single pair of features has been studied in some detail, but may be limited in importance or general applicability. In contrast, testing equality of covariance matrices of a {\it set} of…
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…
In this paper we study the problem of measuring and testing joint independence for a collection of multivariate random variables. Using the emerging theory of optimal transport (OT) based multivariate ranks, we propose a distribution-free…
The problem of testing changes in covariance has received increasing attention in recent years, especially in the context of high-dimensional testing. A number of approaches have been proposed, all limited to the two-sample problem and…
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…
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…
A new method based on the rejection sampling for finding statistical tests is proposed. This method is conceptually intuitive, easy to implement, and applicable for arbitrary dimension. To illustrate its potential applicability, three…
We investigate the problem of detecting dependencies between the components of a high-dimensional vector. Our approach advances the existing literature in two important respects. First, we consider the problem under privacy constraints.…
Testing mutual independence among multiple random variables is a fundamental problem in statistics, with wide applications in genomics, finance, and neuroscience. In this paper, we propose a new class of tests for high-dimensional mutual…
For a set of dependent random variables, without stationary or the strong mixing assumptions, we derive the asymptotic independence between their sums and maxima. Then we apply this result to high-dimensional testing problems, where we…
In this paper new tests for the independence of two high-dimensional vectors are investigated. We consider the case where the dimension of the vectors increases with the sample size and propose multivariate analysis of variance-type…
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 need to test whether two random vectors are independent has spawned a large number of competing measures of dependence. We are interested in nonparametric measures that are invariant under strictly increasing transformations, such as…
We take a different look at the problem of testing the independence of two metric-space-valued random variables using the distance correlation. Instead of testing if the distance correlation vanishes exactly, we are interested in the…
Measuring a strength of dependence of random variables is an important problem in statistical practice. In this paper, we propose a new function valued measure of dependence of two random variables. It allows one to study and visualize…
We propose a simple multivariate normality test based on Kac-Bernstein's characterization, which can be conducted by utilising existing statistical independence tests for sums and differences of data samples. We also perform its empirical…
Asymptotic properties of a dimension-robust dependence measure are investigated. It is related to those used in independence tests, but is derivable, thus suitable for independent component analysis. An adjustable kernel allows to…
Although unbiasedness is a basic property of a good test, many tests on vector parameters or scalar parameters against two-sided alternatives are not finite-sample unbiased. This was already noticed by Sugiura [Ann. Inst. Statist. Math. 17…