Related papers: Measuring Association between Random Vectors
We propose two classes of nonparametric point estimators of $\theta=P(X<Y)$ in the case where $(X,Y)$ are paired, possibly dependent, absolutely continuous random variables. The proposed estimators are based on nonparametric estimators of…
We construct and analyze an estimator of association between random variables based on their similarity in both direction and magnitude. Under special conditions, the proposed measure becomes a robust and consistent estimator of the linear…
In many practical scenarios, including finance, environmental sciences, system reliability, etc., it is often of interest to study the various notion of negative dependence among the observed variables. A new bivariate copula is proposed…
In this work, we propose extropy measures based on density copula, distributional copula, and survival copula, and explore their properties. We study the effect of monotone transformations for the proposed measures and obtain bounds. We…
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…
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…
The assessment of monotone dependence between random variables $X$ and $Y$ is a classical problem in statistics and a gamut of application domains. Consequently, researchers have sought measures of association that are invariant under…
We introduce a novel measure of dependence that captures the extent to which a random variable $Y$ is determined by a random vector $X$. The measure equals zero precisely when $Y$ and $X$ are independent, and it attains one exactly when $Y$…
Improving the detection of relevant variables using a new bivariate measure could importantly impact variable selection and large network inference methods. In this paper, we propose a new statistical coefficient that we call the rank…
Distance correlation is a novel class of multivariate dependence measure, taking positive values between 0 and 1, and applicable to random vectors of arbitrary dimensions, not necessarily equal. It offers several advantages over the…
The partial correlation coefficient is a commonly used measure to assess the conditional dependence between two random variables. We provide a thorough explanation of the partial copula, which is a natural generalization of the partial…
We describe here a new method to estimate copula measure. From N observations of two variables X and Y, we draw a huge number m of subsamples (size n<N), and we compute the joint ranks in these subsamples. Then, for each bivariate rank…
This paper begins the exploration of what we call measures of association between two irreducible complex projective varieties of the same dimension. The idea is to study from various points of view the minimal complexity of correspondences…
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…
In the present paper, we propose a new rank correlation coefficient $r_n$, which is a sample analogue of the theoretical correlation coefficient $r$, which, in turn, was proposed in the recent work of Stepanov (2025b). We discuss the…
Spatial association measures for univariate static spatial data are widely used. When the data is in the form of a collection of spatial vectors with the same temporal domain of interest, we construct a measure of similarity between the…
We study the problem of rank aggregation: given a set of ranked lists, we want to form a consensus ranking. Furthermore, we consider the case of extreme lists: i.e., only the rank of the best or worst elements are known. We impute missing…
In this paper, a class of statistics named ART (the alternant recursive topology statistics) is proposed to measure the properties of correlation between two variables. A wide range of bi-variable correlations both linear and nonlinear can…
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 compare measures of concordance that arise as Pearson's linear correlation coefficient between two random variables transformed so that they follow the so-called concordance-inducing distributions. The class of such transformed rank…