Jackknife empirical likelihood ratio test for independence between a continuous and a categorical random variable

The categorical Gini covariance is a measure of dependence between a numerical variable and a categorical variable, quantifying the difference between conditional and unconditional distribution functions. The categorical Gini covariance equals zero if and only if the numerical variable and the categorical variable are independent. Inspired by this property, we propose a non-parametric test to assess the independence between a numerical and categorical variable using a modified version of the categorical Gini covariance. We used the theory of U-statistics to find the test statistics and study the properties. The proposed test has an asymptotic normal distribution under both the null and alternative hypotheses. Since implementing a normal-based test is difficult, we developed a jackknife empirical likelihood (JEL) ratio test for testing independence. Monte Carlo simulation studies are performed to validate the performance of the proposed JEL ratio test. We illustrate the test procedure using two real data sets.