Related papers: On relationships between Chatterjee's and Spearman…
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…
A fundamental task in statistical learning is quantifying the joint dependence or association between two continuous random variables. We introduce a novel, fully non-parametric measure that assesses the degree of association between…
We consider the problem of testing whether pairs of univariate random variables are associated. Few tests of independence exist that are consistent against all dependent alternatives and are distribution free. We propose novel tests that…
Testing cross-sectional independence in panel data models is of fundamental importance in econometric analysis with high-dimensional panels. Recently, econometricians began to turn their attention to the problem in the presence of serial…
In order to address the theoretical challenges arising from the dependence structure of ranks in Spearman's footrule correlation coefficient, we propose two asymptotic representations to approximate the distribution of this coefficient…
In this paper, a robust non-parametric measure of statistical dependence, or correlation, between two random variables is presented. The proposed coefficient is a permutation-like statistic that quantifies how much the observed sample S_n :…
Besides the classical distinction of correlation and dependence, many dependence measures bear further pitfalls in their application and interpretation. The aim of this paper is to raise and recall awareness of some of these limitations by…
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,…
While measures of concordance -- such as Spearman's rho, Kendall's tau, and Blomqvist's beta -- are continuous with respect to weak convergence, Chatterjee's rank correlation xi recently introduced in Azadkia and Chatterjee (2021) does not…
A margin-free measure of bivariate association generalizing Spearman's rho to the case of non-monotonic dependence is defined in terms of two square integrable functions on the unit interval. Properties of generalized Spearman correlation…
A multivariate version of Spearman's rho for testing independence is considered. Its asymptotic efficiency is calculated under a general distribution model specified by the dependence function. The efficiency comparison study that involves…
We introduce a new dependence order, termed the conditional convex order, whose minimal and maximal elements characterize independence and perfect dependence. Moreover, it characterizes conditional independence, satisfies information…
This article proposes a new index for quantifying the degree of dependence between random vectors. The index takes values in [0,1] and equals zero if and only if the random vectors are sub-independent. Unlike mere uncorrelatedness,…
In this paper, we introduce the notion of a ``pairwise independent correlation gap'' for set functions with random elements. The pairwise independent correlation gap is defined as the ratio of the maximum expected value of a set function…
Tests of independence are an important tool in applications, specifically in connection with the detection of a relationship between variables; they also have initiated many developments in statistical theory. In the present paper we build…
Multiple correlation is a fundamental concept with broad applications. The classical multiple correlation coefficient is developed to assess how strongly a dependent variable is associated with a linear combination of independent variables.…
We treat the problem of testing independence between m continuous variables when m can be larger than the available sample size n. We consider three types of test statistics that are constructed as sums or sums of squares of pairwise rank…
Recently, Chatterjee (2023) recognized the lack of a direct generalization of his rank correlation $\xi$ in Azadkia and Chatterjee (2021) to a multi-dimensional response vector. As a natural solution to this problem, we here propose an…
In this paper, we address the problem of testing independence between two high-dimensional random vectors. Our approach involves a series of max-sum tests based on three well-known classes of rank-based correlations. These correlation…
We consider the asymptotic joint distributions among several families of well-known metrics on $S_n$, the symmetric group. These include the bi-invariant metrics such as the Cayley and Hamming distance, and the left-invariant metrics such…