Related papers: A new Gini correlation between quantitative and qu…
Motivated by the importance of measuring the association between the response and predictors in high dimensional data, In this article, we propose a new mean variance test of independence between a categorical random variable and a…
A fundamental task in statistical learning is quantifying the joint dependence or association between two continuous random variables. We introduce a novel, fully non-parametric measure that assesses the degree of association between…
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…
Identifying how dependence relationships vary across different conditions plays a significant role in many scientific investigations. For example, it is important for the comparison of biological systems to see if relationships between…
This paper proposes a new Bayesian approach to estimate the Gini coefficient from the Lorenz curve based on grouped data. The proposed approach assumes a hypothetical income distribution and estimates the parameter by directly working on…
In this paper, the defining properties of a valid measure of the dependence between two random variables are reviewed and complemented with two original ones, shown to be more fundamental than other usual postulates. While other popular…
Gini index is a widely used measure of economic inequality. This article develops a general theory for constructing a confidence interval for Gini index with a specified confidence coefficient and a specified width. Fixed sample size…
Testing two potentially multivariate variables for statistical dependence on the basis finite samples is a fundamental statistical challenge. Here we explore a family of tests that adapt to the complexity of the relationship between the…
In this article, we consider the problem of testing the independence between two random variables. Our primary objective is to develop tests that are highly effective at detecting associations arising from explicit or implicit functional…
The goal of this paper is to design a causal inference method accounting for complex interactions between causal factors. The proposed method relies on a category theoretical reformulation of the definitions of dependent variables,…
Estimating the strength of dependency between two variables is fundamental for exploratory analysis and many other applications in data mining. For example: non-linear dependencies between two continuous variables can be explored with the…
Covariances from categorical variables are defined using a regular simplex expression for categories. The method follows the variance definition by Gini, and it gives the covariance as a solution of simultaneous equations. The calculated…
We examine the efficiency of the mean deviation and Gini's mean difference (the mean of all pairwise distances). Our findings support the viewpoint that Gini's mean difference combines the advantages of the mean deviation and the standard…
Quantile regression, the prediction of conditional quantiles, finds applications in various fields. Often, some or all of the variables are discrete. The authors propose two new quantile regression approaches to handle such mixed…
The Gini index is a widely reported measure of income inequality. In some settings, the underlying data used to compute the Gini index are confidential. The organization charged with reporting the Gini index may be concerned that its…
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…
This paper introduces the correlation-of-divergency coefficient, c-delta, a custom statistical measure designed to quantify the similarity of internal divergence patterns between two groups of values. Unlike conventional correlation…
Testing independence among a number of (ultra) high-dimensional random samples is a fundamental and challenging problem. By arranging $n$ identically distributed $p$-dimensional random vectors into a $p \times n$ data matrix, we investigate…
Many relations of scientific interest are nonlinear, and even in linear systems distributions are often non-Gaussian, for example in fMRI BOLD data. A class of search procedures for causal relations in high dimensional data relies on sample…
The dilemma which remained unsolved using Rao-Stirling diversity, namely of how variety and balance can be combined into "dual concept diversity" (Stirling, 1998, pp. 48f.) can be clarified by using Nijssen et al.'s (1998) argument that the…