Related papers: On Correlation Coefficients
The correlation between NLG automatic evaluation metrics and human evaluation is often regarded as a critical criterion for assessing the capability of an evaluation metric. However, different grouping methods and correlation coefficients…
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…
Recently, Chatterjee has introduced a new coefficient of correlation which has several natural properties. In particular, the coefficient attains its maximal value if and only if one variable is a measurable function of the other variable.…
The difficulties of detecting association, measuring correlation, and establishing cause and effect have fascinated mankind since time immemorial. Democritus, the Greek philosopher, underscored well the importance and the difficulty of…
Distance covariance and distance correlation are scalar coefficients that characterize independence of random vectors in arbitrary dimension. Properties, extensions, and applications of distance correlation have been discussed in the recent…
There has been an increasing interest in testing the equality of large Pearson's correlation matrices. However, in many applications it is more important to test the equality of large rank-based correlation matrices since they are more…
This article proposes a new index for quantifying the degree of dependence between random vectors. The index takes values in [0,1] and equals zero if and only if the random vectors are sub-independent. Unlike mere uncorrelatedness,…
This article proposes an improved version of the Spearman rank correlation based on using Wilcoxon rank score function. A smoothed empirical cumulative distribution function (ecdf)computes the smoothed ranks and replaces the regular ranks…
This work is concerned with the limiting spectral distribution of rank-based dependency measures in high dimensions. We provide distribution-free results for multivariate empirical versions of Kendall's $\tau$ and Spearman's $\rho$ in a…
A useful property of independent samples is that their correlation remains the same after applying marginal transforms. This invariance property plays a fundamental role in statistical inference, but does not hold in general for dependent…
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…
For a bivariate time series $((X_i,Y_i))_{i=1,...,n}$ we want to detect whether the correlation between $X_i$ and $Y_i$ stays constant for all $i = 1,...,n$. We propose a nonparametric change-point test statistic based on Kendall's tau and…
Conditional independence (CI) testing arises naturally in many scientific problems and applications domains. The goal of this problem is to investigate the conditional independence between a response variable $Y$ and another variable $X$,…
Re-sampling based statistical tests are known to be computationally heavy, but reliable when small sample sizes are available. Despite their nice theoretical properties not much effort has been put to make them efficient. In this paper we…
In this paper, we address the problem of testing independence between two high-dimensional random vectors. Our approach involves a series of max-sum tests based on three well-known classes of rank-based correlations. These correlation…
(To appear in The American Statistician.) Distance covariance (Sz\'ekely, Rizzo, and Bakirov, 2007) is a fascinating recent notion, which is popular as a test for dependence of any type between random variables $X$ and $Y$. This approach…
Reliably measuring the collinearity of bivariate data is crucial in statistics, particularly for time-series analysis or ongoing studies in which incoming observations can significantly impact current collinearity estimates. Leveraging…
Distance correlation is a new measure of dependence between random vectors. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but unlike the classical definition of correlation,…
This paper is concerned with Spearman's correlation matrices under large dimensional regime, in which the data dimension diverges to infinity proportionally with the sample size. We establish the central limit theorem for the linear…
It has been recently shown in Jaworski, P., Jelito, D. and Pitera, M. (2024), 'A note on the equivalence between the conditional uncorrelation and the independence of random variables', Electronic Journal of Statistics 18(1), that one can…