Jackknife empirical likelihood confidence intervals for the categorical Gini correlation

The categorical Gini correlation, ${\rho }_g$, was proposed by Dang et al. (2021) 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.