JEL ratio test for independence between a continuous and a categorical random variable

Abstract: The categorical Gini covariance is a dependence measure between a numerical variable and a categorical variable. The Gini covariance measures dependence by quantifying the difference between the conditional and unconditional distributional functions. The categorical Gini covariance equals zero if and only if the numerical variable and the categorical variable are independent. We propose a non-parametric test for testing the independence between a numerical and categorical variable using a modified categorical Gini covariance. We used the theory of U-statistics to find the test statistics and study the properties. The test has an asymptotic normal distribution. Since the implementation of a normal-based test is difficult, we develop a jackknife empirical likelihood (JEL) ratio test for testing independence. Extensive Monte Carlo simulation studies are carried out to validate the performance of the proposed JEL ratio test. We illustrate the test procedure using Iris flower data set.