Jackknife empirical likelihood confidence intervals for the categorical Gini correlation

TL;DR

This paper introduces a jackknife empirical likelihood approach to construct confidence intervals for the categorical Gini correlation, offering a variance-free method with improved performance over existing techniques.

Contribution

It develops the first JEL-based confidence interval method for the categorical Gini correlation, including adjusted and weighted versions for enhanced accuracy.

Findings

Methods achieve competitive coverage accuracy.

Confidence intervals are shorter and more reliable.

Application to real datasets demonstrates practical utility.

Abstract

The categorical Gini correlation, $\rho_g$, was proposed by Dang et al. to measure the dependence between a categorical variable, $Y$ , and a numerical variable, $X$. It has been shown that $\rho_g$ has more appealing properties than current existing dependence measurements. In this paper, we develop the jackknife empirical likelihood (JEL) method for $\rho_g$. Confidence intervals for the Gini correlation are constructed without estimating the asymptotic variance. Adjusted and weighted JEL are explored to improve the performance of the standard JEL. Simulation studies show that our methods are competitive to existing methods in terms of coverage accuracy and shortness of confidence intervals. The proposed methods are illustrated in an application on two real datasets.