Related papers: Measuring Association between Random Vectors
We introduce a new measure of interdependence among the components of a random vector along the main diagonal of the vector copula, i.e. along the line $u_{1}=\ldots=u_{J}$, for $\left(u_{1},\ldots,u_{J}\right)\in\left[0,1\right]^{J}$. Our…
Many statistical applications require the quantification of joint dependence among more than two random vectors. In this work, we generalize the notion of distance covariance to quantify joint dependence among d >= 2 random vectors. We…
Studying the multivariate extension of copula correlation yields a dimension reduction principle, which turns out to be strongly related with the `simple measure of conditional dependence' $T$ recently introduced by Azadkia & Chatterjee…
Results in epidemiology and social science often require the removal of confounding effects from measurements of the pairwise correlation of variables in survey data. This is typically accomplished by some variant of linear regression…
Rank-rank regression is commonly employed in economic research as a way of capturing the relationship between two economic variables. The slope of this regression is the Spearman rank correlation, a classical measure of association.…
We explore the consequences of a set of axioms which extend Scarsini's axioms for bivariate measures of concordance to the multivariate case and exhibit the following results: (1) A method of extending measures of concordance from the…
We investigate patterns of assortative matching on risk attitude, using self-reported (ordinal) data on risk attitudes for males and females within married couples, from the German Socio-Economic Panel over the period 2004-2012. We apply a…
In this investigation, the distribution of the ratio of two independently distributed xgamma (Sen et al. 2016) random variables X and Y , with different parameters, is proposed and studied. The related distributional properties such as,…
The reliability of machine learning systems critically assumes that the associations between features and labels remain similar between training and test distributions. However, unmeasured variables, such as confounders, break this…
The relation between Pearson's correlation coefficient and Salton's cosine measure is revealed based on the different possible values of the division of the L1-norm and the L2-norm of a vector. These different values yield a sheaf of…
An overview of existing nonparametric tests of extreme-value dependence is presented. Given an i.i.d.\ sample of random vectors from a continuous distribution, such tests aim at assessing whether the underlying unknown copula is of the {\em…
This study explores information measures based on extropy, introducing dynamic relative extropy measures for residual and past lifetimes, and investigating their various properties. Furthermore, the study analyzes the relationships between…
A new description of strange attractor systems through three geometrical and dynamical invariants is provided. They are the correlation dimension ($\mathcal{D}$) and the correlation entropy ($\mathcal{K}$), both having attracted attention…
Causal discovery estimates the underlying physical process that generates the observed data: does X cause Y or does Y cause X? Current methodologies use structural conditions to turn the causal query into a statistical query, when only…
The problem of detecting changes in covariance for a single pair of features has been studied in some detail, but may be limited in importance or general applicability. In contrast, testing equality of covariance matrices of a {\it set} of…
Associative measures are "mathematical formulas determining the strength of association between two or more words based on their occurrences and cooccurrences in a text corpus" (Pecina, 2010, p. 138). The purpose of this paper is to test…
The presence of significant cross-correlations between the synchronous time evolution of a pair of equity returns is a well-known empirical fact. The Pearson correlation is commonly used to indicate the level of similarity in the price…
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…
New nonparametric tests of copula exchangeability and radial symmetry are proposed. The novel aspect of the tests is a resampling procedure that exploits group invariance conditions associated with the relevant symmetry hypothesis. They may…
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.…