Related papers: Adjust Pearson's $r$ to Measure Arbitrary Monotone…
The Pearson-Matthews correlation coefficient (usually abbreviated MCC) is considered to be one of the most useful metrics for the performance of a binary classification or hypothesis testing method (for the sake of conciseness we will use…
Through computer simulations, we research several different measures of dependence, including Pearson's and Spearman's correlation coefficients, the maximal correlation, the distance correlation, a function of the mutual information called…
Motivated by the pressing needs for capturing complex but interpretable variable relationships in scientific research, here we generalize the squared Pearson correlation to capture a mixture of linear dependences between two real-valued…
The Hirschfeld-Gebelein-R\'enyi (HGR) correlation coefficient is an extension of Pearson's correlation that is not limited to linear correlations, with potential applications in algorithmic fairness, scientific analysis, and causal…
Measuring and quantifying dependencies between random variables (RV's) can give critical insights into a data-set. Typical questions are: `Do underlying relationships exist?', `Are some variables redundant?', and `Is some target variable…
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…
Testing independence among a number of (ultra) high-dimensional random samples is a fundamental and challenging problem. By arranging $n$ identically distributed $p$-dimensional random vectors into a $p \times n$ data matrix, we investigate…
A useful property of independent samples is that their correlation remains the same after applying marginal transforms. This invariance property plays a fundamental role in statistical inference, but does not hold in general for dependent…
Accurately estimating the proportion of true signals among a large number of variables is crucial for enhancing the precision and reliability of scientific research. Traditional signal proportion estimators often assume independence among…
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…
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…
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.…
George R. Terrell (1983, {Ann. Probab., vol. 11(3), pp. 823--826) showed that the Pearson coefficient of correlation of an ordered pair from a random sample of size two is at most one-half, and the equality is attained only for rectangular…
Couplings in complex real-world systems are often nonlinear and scale-dependent. In many cases, it is crucial to consider a multitude of interlinked variables and the strengths of their correlations to adequately fathom the dynamics of a…
In network theory, Pearson's correlation coefficients are most commonly used to measure the degree assortativity of a network. We investigate the behavior of these coefficients in the setting of directed networks with heavy-tailed degree…
We investigate the possible drawbacks of employing the standard Pearson estimator to measure correlation coefficients between financial stocks in the presence of non-stationary behavior, and we provide empirical evidence against the…
This article examines the limitations of Pearson's correlation in selecting predictor variables for linear models. Using mtcars and iris datasets from R, this paper demonstrates the limitation of this correlation measure when selecting a…
Mixing patterns in large self-organizing networks, such as the Internet, the World Wide Web, social and biological networks are often characterized by degree-degree {dependencies} between neighbouring nodes. One of the problems with the…
We introduce the Randomized Dependence Coefficient (RDC), a measure of non-linear dependence between random variables of arbitrary dimension based on the Hirschfeld-Gebelein-R\'enyi Maximum Correlation Coefficient. RDC is defined in terms…
Linear regression is a frequently used tool in statistics, however, its validity and interpretability relies on strong model assumptions. While robust estimates of the coefficients' covariance extend the validity of hypothesis tests and…