Related papers: Correlations with tailored extremal properties
Chatterjee's correlation coefficient has recently been proposed as a new association measure for bivariate random vectors that satisfies a number of desirable properties. Among these properties is the feature that the coefficient equals one…
The maximum correlation of functions of a pair of random variables is an important measure of stochastic dependence. It is known that this maximum nonlinear correlation is identical to the absolute value of the Pearson correlation for a…
How to understand the set of correlations admissible in nature is one outstanding open problem in the core of the foundations of quantum theory. Here we take a complementary viewpoint to the device-independent approach, and explore the…
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…
Establishing the limiting distribution of Chatterjee's rank correlation for a general, possibly non-independent, pair of random variables has been eagerly awaited by many. This paper shows that (a) Chatterjee's rank correlation is…
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 coefficient that measures dependence in paired samples of functions. It has properties similar to the Pearson correlation, but differs in significant ways: (i) it is designed to measure dependence between curves, (ii) it…
Building upon the Chatterjee correlation (2021: J. Am. Stat. Assoc. 116, p2009) for two real-valued variables, this study introduces a generalized measure of directed association between two vector variables, real or complex-valued, and of…
Chatterjee's rank correlation is a directed measure of association designed to detect whether one variable can be predicted as a function of another. While the original coefficient is naturally defined for real-valued data, circular data…
Quantifying the strength of functional dependence between random scalars $X$ and $Y$ is an important statistical problem. While many existing correlation coefficients excel in identifying linear or monotone functional dependence, they fall…
The Pearson correlation, correlation ratio, and maximal correlation have been well-studied in the literature. In this paper, we study the conditional versions of these quantities. We extend the most important properties of the unconditional…
We introduce a new type of influence function, the asymptotic expected sensitivity function, which is often equivalent to but mathematically more tractable than the traditional one based on the Gateaux derivative. To illustrate, we study…
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…
A random coefficient autoregressive process is deeply investigated in which the coefficients are correlated. First we look at the existence of a strictly stationary causal solution, we give the second-order stationarity conditions and the…
We suggest novel correlation coefficients which equal the maximum correlation for a class of bivariate Lancaster distributions while being only slightly smaller than maximum correlation for a variety of further bivariate distributions. In…
Chatterjee (2021) introduced an asymmetric correlation measure that has attracted much attention over the past year. In this paper, we derive the asymptotic distribution of the symmetric version of Chatterjee's correlation, and suggest a…
Based on the notion of maximal correlation, Kimeldorf, May and Sampson (1980) introduce a measure of correlation between two random variables, called the "concordant monotone correlation" (CMC). We revisit, generalize and prove new…
We prove that a suitably de-biased version of Chatterjee's rank correlation based on i.i.d. copies of a random vector $(X,Y)$ is asymptotically normal whenever $Y$ is not almost surely constant. No further conditions on the joint…
We consider the correlation functions of eigenvalues of a unidimensional chain of large random hermitian matrices. An asymptotic expression of the orthogonal polynomials allows to find new results for the correlations of eigenvalues of…
Recently, Chatterjee (2021) introduced a new rank-based correlation coefficient which can be used to measure the strength of dependence between two random variables. This coefficient has already attracted much attention as it converges to…