Related papers: Symmetric Gini Covariance and Correlation
Measuring strength or degree of statistical dependence between two random variables is a common problem in many domains. Pearson's correlation coefficient $\rho$ is an accurate measure of linear dependence. We show that $\rho$ is a…
Estimating the correlation coefficient has been a daunting work with the increasing complexity of dataset's pattern. One of the problems in manufacturing applications consists of the estimation of a critical process variable during a…
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…
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…
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…
Representations of measures of concordance in terms of Pearson' s correlation coefficient are studied. All transforms of random variables are characterized such that the correlation coefficient of the transformed random variables is a…
The Gini score is a popular tool in statistical modeling and machine learning for model validation and model selection. It is a purely rank based score that allows one to assess risk rankings. The Gini score for statistical modeling has…
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…
Direct measurements of Gini coefficients by conventional arithmetic calculations are a poor estimator, even if paradoxically, they include the entire population, as because of super-additivity they cannot lend themselves to comparisons…
The covariance of two random variables measures the average joint deviations from their respective means. We generalise this well-known measure by replacing the means with other statistical functionals such as quantiles, expectiles, or…
Extremal dependence describes the strength of correlation between the largest observations of two variables. It is usually measured with symmetric dependence coefficients that do not depend on the order of the variables. In many cases,…
Quantifying concordance between two random variables is crucial in applications. Traditional estimation techniques for commonly used concordance measures, such as Gini's gamma or Spearman's rho, often fail when data contain ties. This is…
A principal component analysis based on the generalized Gini correlation index is proposed (Gini PCA). The Gini PCA generalizes the standard PCA based on the variance. It is shown, in the Gaussian case, that the standard PCA is equivalent…
Model attributions are important in deep neural networks as they aid practitioners in understanding the models, but recent studies reveal that attributions can be easily perturbed by adding imperceptible noise to the input. The…
Detecting dependence between two random variables is a fundamental problem. Although the Pearson correlation is effective for capturing linear dependency, it can be entirely powerless for detecting nonlinear and/or heteroscedastic patterns.…
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…
The quotient correlation is defined here as an alternative to Pearson's correlation that is more intuitive and flexible in cases where the tail behavior of data is important. It measures nonlinear dependence where the regular correlation…
Pearson's is the most common correlation statistic, used mainly in parametric settings. Most common among nonparametric correlation statistics are Spearman's and Kendall's. We show that for bivariate normal i.i.d. samples the pairwise…
Classical dependence measures such as Pearson correlation, Spearman's $\rho$, and Kendall's $\tau$ can detect only monotonic or linear dependence. To overcome these limitations, Szekely et al.(2007) proposed distance covariance as a…
Pearson's $\rho$ is the most used measure of statistical dependence. It gives a complete characterization of dependence in the Gaussian case, and it also works well in some non-Gaussian situations. It is well known, however, that it has a…