Related papers: Measuring Association between Random Vectors
We extend some of the measures of association defined by Lazarsfeld and Martin, obtaining useful invariants to compare the birational geometry of two varieties having different dimensions. We explore such invariants providing examples and…
This paper proposes a new mutual independence test for a large number of high dimensional random vectors. The test statistic is based on the characteristic function of the empirical spectral distribution of the sample covariance matrix. The…
A class of tests for change-point detection designed to be particularly sensitive to changes in the cross-sectional rank correlation of multivariate time series is proposed. The derived procedures are based on several multivariate…
In this article, we propose a new nonparametric data analysis tool, which we call nonparametric modal regression, to investigate the relationship among interested variables based on estimating the mode of the conditional density of a…
Copulas are becoming an essential tool in analyzing data thus encouraging interest in related questions. In the early stage of exploratory data analysis, say, it is helpful to know local copula bounds with a fixed value of a given measure…
This paper formulates and evaluates a series of multi-unit measures of directional association, building on the pairwise {\Delta}P measure, that are able to quantify association in sequences of varying length and type of representation.…
Based on recent progress in research on copula based dependence measures, we review the original Renyi's axioms on symmetric measures and propose a new set of axioms that applies to nonsymmetric measures. We show that nonsymmetric measures…
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 propose a method for summarizing the strength of association between a set of variables and a multivariate outcome. Classical summary measures are appropriate when linear relationships exist between covariates and outcomes, while our…
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,…
Measuring the (causal) direction and strength of dependence between two variables (events), Xi and Xj , is fundamental for all science. Our survey of decades-long literature on statistical dependence reveals that most assume symmetry in the…
The extension of bivariate measures of dependence to non-Euclidean spaces is a challenging problem. The non-linear nature of these spaces makes the generalisation of classical measures of linear dependence (such as the covariance) not…
Assessing agreement between two instruments is crucial in clinical studies to evaluate the similarity between two methods measuring the same subjects. This paper introduces a novel coefficient, termed rho1, to measure agreement between…
Association models for a pair of random elements $X$ and $Y$ (e.g., vectors) are considered which specify the odds ratio function up to an unknown parameter $\bolds\theta$. These models are shown to be semiparametric in the sense that they…
The Pearson product-moment correlation coefficient (rp) and the Spearman rank correlation coefficient (rs) are widely used in psychological research. We compare rp and rs on 3 criteria: variability, bias with respect to the population…
This article presents several alternatives to Pearson's correlation coefficient and many examples. In the samples where the rank in a discrete variable counts more than the variable values, the mixtures that we propose of Pearson's and…
In his seminal work, Chatterjee (2021) introduced a novel correlation measure which is distribution-free, asymptotically normal, and consistent against all alternatives. In this paper, we study the probabilistic relationships between…
We propose a new measure related with tail dependence in terms of correlation: quantile correlation coefficient of random variables X, Y. The quantile correlation is defined by the geometric mean of two quantile regression slopes of X on Y…
Rank-based dependence measures such as Spearman's footrule are robust and invariant, but they often fail to capture directional or asymmetric dependence in multivariate settings. This paper introduces a new family of directional Spearman's…
In the present paper we propose and study estimators for a wide class of bivariate measures of concordance for copulas. These measures of concordance are generated by a copula and generalize Spearman's rho and Gini's gamma. In the case of…