Related papers: Alternatives to Pearson's and Spearman's Correlati…
The maximal correlation coefficient is a well-established generalization of the Pearson correlation coefficient for measuring non-linear dependence between random variables. It is appealing from a theoretical standpoint, satisfying…
Clustered data are common in practice. Clustering arises when subjects are measured repeatedly, or subjects are nested in groups (e.g., households, schools). It is often of interest to evaluate the correlation between two variables with…
Spearman's rank correlation test is commonly used in astronomy to discern whether a set of two variables are correlated or not. Unlike most other quantities quoted in astronomical literature, the Spearman's rank correlation coefficient is…
The Pearson correlation, correlation ratio, and maximal correlation have been well-studied in the literature. In this paper, we study the conditional versions of these quantities. We extend the most important properties of the unconditional…
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…
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…
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…
In this paper, we propose two new estimators of the multivariate rank correlation coefficient Spearman's footrule which are based on two general estimators for Average Orthant Dependence measures. We compare the new proposals with a…
The partial correlation coefficient is a commonly used measure to assess the conditional dependence between two random variables. We provide a thorough explanation of the partial copula, which is a natural generalization of the partial…
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…
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…
Copula models have been widely used to model the dependence between continuous random variables, but modeling count data via copulas has recently become popular in the statistics literature. Spearman's rho is an appropriate and effective…
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…
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…
The Pearson correlation coefficient is commonly used for quantifying the global level of degree-degree association in complex networks. Here, we use a probabilistic representation of the underlying network structure for assessing the…
We study Sharp Large Deviations for Pearson's empirical correlation coefficients in the Spherical and Gaussian cases
The Particle Data Group recommends a set of procedures to be applied when discrepant data are to be combined. We introduce an alternative method based on a more general and solid statistical framework, providing a robust way to include…
Presented is an inductive formula for computing the sample moments of the distribution of Pearson's sample correlation over permutation of data. These exact formulas for the sample moments suggest the possibility of more precise and…
Improving the detection of relevant variables using a new bivariate measure could importantly impact variable selection and large network inference methods. In this paper, we propose a new statistical coefficient that we call the rank…
Pearson's correlation coefficient is a popular statistical measure to summarize the strength of association between two continuous variables. It is usually interpreted via its square as percentage of variance of one variable predicted by…