Related papers: A new measure of dependence: Integrated $R^2$
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…
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,…
Measuring conditional dependencies among the variables of a network is of great interest to many disciplines. This paper studies some shortcomings of the existing dependency measures in detecting direct causal influences or their lack of…
In this paper, the maximal nonlinear conditional correlation of two random vectors $X$ and $Y$ given another random vector $Z$, denoted by $\rho_1(X,Y|Z)$, is defined as a measure of conditional association, which satisfies certain…
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…
In this paper, the defining properties of a valid measure of the dependence between two random variables are reviewed and complemented with two original ones, shown to be more fundamental than other usual postulates. While other popular…
We propose a coefficient of conditional dependence between two random variables $Y$ and $Z$ given a set of other variables $X_1,\ldots,X_p$, based on an i.i.d. sample. The coefficient has a long list of desirable properties, the most…
Most of the popular dependence measures for two random variables $X$ and $Y$ (such as Pearson's and Spearman's correlation, Kendall's $\tau$ and Gini's $\gamma$) vanish whenever $X$ and $Y$ are independent. However, neither does a vanishing…
We introduce kernel integrated $R^2$, a new measure of statistical dependence that combines the local normalization principle of the recently introduced integrated $R^2$ with the flexibility of reproducing kernel Hilbert spaces (RKHSs). The…
A coefficient is introduced that quantifies the extent of separation of a random variable $Y$ relative to a number of variables $\mathbf{X} = (X_1, \dots, X_p)$ by skillfully assessing the sensitivity of the relative effects of the…
This paper develops an intuitive concept of perfect dependence between two variables of which at least one has a nominal scale. Perfect dependence is attainable for all marginal distributions. It furthermore proposes a set of dependence…
In this paper we introduce a new measure of conditional dependence between two random vectors ${\boldsymbol X}$ and ${\boldsymbol Y}$ given another random vector $\boldsymbol Z$ using the ball divergence. Our measure characterizes…
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…
Dependence is undoubtedly a central concept in statistics. Though, it proves difficult to locate in the literature a formal definition which goes beyond the self-evident 'dependence = non-independence'. This absence has allowed the term…
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…
The maximal correlation coefficient is a well-established generalization of the Pearson correlation coefficient for measuring non-linear dependence between random variables. It is appealing from a theoretical standpoint, satisfying…
Is it possible to define a coefficient of correlation which is (a) as simple as the classical coefficients like Pearson's correlation or Spearman's correlation, and yet (b) consistently estimates some simple and interpretable measure of the…
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,…
As a crucial problem in statistics is to decide whether additional variables are needed in a regression model. We propose a new multivariate test to investigate the conditional mean independence of Y given X conditioning on some known…
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…