Related papers: Statistical dependence: Beyond Pearson's $\rho$
Besides the classical distinction of correlation and dependence, many dependence measures bear further pitfalls in their application and interpretation. The aim of this paper is to raise and recall awareness of some of these limitations by…
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…
Measuring dependence between random variables is a fundamental problem in Statistics, with applications across diverse fields. While classical measures such as Pearson's correlation have been widely used for over a century, they have…
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…
Pearson's correlation is one of the most common measures of linear dependence. Recently, Bernardo (2015) introduced a flexible class of priors to study this measure in a Bayesian setting. For this large class of priors we show that the…
Distance correlation is a recent extension of Pearson's correlation, that characterises general statistical independence between Euclidean-space-valued random variables, not only linear relations. This review delves into how and when…
Not a matter of serious contention, Pearson's correlation coefficient is still the most important statistical association measure. Restricted to just two variables, this measure sometimes doesn't live up to users' needs and expectations.…
Testing the independence between random vectors is a fundamental problem in statistics. Distance correlation, a recently popular dependence measure, is universally consistent for testing independence against all distributions with finite…
In the present paper, we discuss the Pearson, Spearman, Kendall correlation coefficients and their statistical analogues. We propose a new correlation coefficient r and its statistical analogue. The coefficient r is based on Kendal's and…
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 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…
Over the last couple of decades, several copula based methods have been proposed in the literature to test for the independence among several random variables. But these existing tests are not invariant under monotone transformations of 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.…
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…
We develop correlated random measures, random measures where the atom weights can exhibit a flexible pattern of dependence, and use them to develop powerful hierarchical Bayesian nonparametric models. Hierarchical Bayesian nonparametric…
Pearson's r, the most widely-used correlation coefficient, is traditionally regarded as exclusively capturing linear dependence, leading to its discouragement in contexts involving nonlinear relationships. However, recent research…
Background and Objective: Histograms and Pearson's coefficient of variation are among the most popular summary statistics. Researchers use histograms to judge the shape of quantitative data distribution by visual inspection. The coefficient…
Pearson's correlation is an important summary measure of the amount of dependence between two variables. It is natural to want to generalise the concept of correlation as a single number that measures the inter-relatedness of three or more…
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…
We investigate the relative information content of six measures of dependence between two random variables $X$ and $Y$ for large or extreme events for several models of interest for financial time series. The six measures of dependence are…