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Related papers: Notes on the interpretation of dependence measures

200 papers

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…

Statistics Theory · Mathematics 2017-05-01 Alexander Ly , Maarten Marsman , Eric-Jan Wagenmakers

Classical and more recent tests for detecting distributional changes in multivariate time series often lack power against alternatives that involve changes in the cross-sectional dependence structure. To be able to detect such changes…

Statistics Theory · Mathematics 2014-09-16 Axel Bücher , Ivan Kojadinovic , Tom Rohmer , Johan Segers

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…

Methodology · Statistics 2024-09-10 Mustafa Attallah

The concept of distance covariance/correlation was introduced recently to characterize dependence among vectors of random variables. We review some statistical aspects of distance covariance/correlation function and we demonstrate its…

Methodology · Statistics 2018-07-13 Dominic Edelmann , Konstantinos Fokianos , Maria Pitsillou

Simple correlation coefficients between two variables have been generalized to measure association between two matrices in many ways. Coefficients such as the RV coefficient, the distance covariance (dCov) coefficient and kernel based…

Methodology · Statistics 2014-08-19 Julie Josse , Susan Holmes

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.…

Methodology · Statistics 2016-11-21 Xufei Wang , Bo Jiang , Jun S. Liu

Recognizing, quantifying and visualizing associations between two variables is increasingly important. This paper investigates how a new function-valued measure of dependence, the quantile dependence function, can be used to construct tests…

Methodology · Statistics 2019-04-16 Ćmiel Bogdan , Ledwina Teresa

The paper presents a new copula based method for measuring dependence between random variables. Our approach extends the Maximum Mean Discrepancy to the copula of the joint distribution. We prove that this approach has several advantageous…

Machine Learning · Computer Science 2019-08-15 Barnabas Poczos , Zoubin Ghahramani , Jeff Schneider

The distance covariance of two random vectors is a measure of their dependence. The empirical distance covariance and correlation can be used as statistical tools for testing whether two random vectors are independent. We propose an analogs…

Statistics Theory · Mathematics 2017-03-31 Muneya Matsui , Thomas Mikosch , Gennady Samorodnitsky

The multivariate Hilbert-Schmidt-Independence-Criterion (dHSIC) and distance multivariance allow to measure and test independence of an arbitrary number of random vectors with arbitrary dimensions. Here we define versions which only depend…

Statistics Theory · Mathematics 2020-04-17 Björn Böttcher

Measuring dependence between two events, or equivalently between two binary random variables, amounts to expressing the dependence structure inherent in a $2\times 2$ contingency table in a real number between $-1$ and $1$. Countless such…

Methodology · Statistics 2025-11-13 Marc-Oliver Pohle , Timo Dimitriadis , Jan-Lukas Wermuth

Quantification of relations between measured variables of interest by statistical measures of dependence is a common step in analysis of climate data. The term "connectivity" is used in the network context including the study of complex…

Methodology · Statistics 2015-06-12 Jaroslav Hlinka , David Hartman , Martin Vejmelka , Dagmar Novotná , Milan Paluš

A margin-free measure of bivariate association generalizing Spearman's rho to the case of non-monotonic dependence is defined in terms of two square integrable functions on the unit interval. Properties of generalized Spearman correlation…

Methodology · Statistics 2025-12-12 Alexander J. McNeil , Johanna G. Neslehova , Andrew D. Smith

Copulas are mathematical objects that fully capture the dependence structure among random variables and hence, offer a great flexibility in building multivariate stochastic models. In statistics, a copula is used as a general way of…

Methodology · Statistics 2013-10-01 Abhik Ghosh , Aritra Chakravorty

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…

Statistics Theory · Mathematics 2024-05-28 Alexei Stepanov

Following our previous work on copula-based nonsymmetric dependence measures, we introduce similar measures for discrete random variables. The measures cover the range between two extremes: independence and complete dependence, which take…

Methodology · Statistics 2015-12-29 Hui Li

Categorical variables are of uttermost importance in biomedical research. When two of them are considered, it is often the case that one wants to test whether or not they are statistically dependent. We show weaknesses of classical methods…

Inferring linear relationships lies at the heart of many empirical investigations. A measure of linear dependence should correctly evaluate the strength of the relationship as well as qualify whether it is meaningful for the population.…

Methodology · Statistics 2022-08-16 Kaustubh R. Patil , Simon B. Eickhoff , Robert Langner

Spherical and hyperspherical data are commonly encountered in diverse applied research domains, underscoring the vital task of assessing independence within such data structures. In this context, we investigate the properties of test…

Methodology · Statistics 2024-01-23 Marija Cuparić , Bruno Ebner , Bojana Milošević

This study outlines a comprehensive methodology utilizing copulas to discern inconsistencies in the behavior exhibited by pairs of financial assets. It introduces a robust approach to establishing the interrelationship between the returns…

Computational Finance · Quantitative Finance 2023-12-05 Alexander Shulzhenko