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. A value of zero for the categorical Gini covariance implies independence of the numerical variable and the categorical variable. We propose a non-parametric test for testing the independence between a numerical and categorical variable using the 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. As 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-based test. We illustrate the test procedure using real a data set.

翻译：分类Gini协方差是一种衡量数值变量与分类变量之间依赖关系的指标。该指标通过量化条件分布函数与无条件分布函数之间的差异来度量依赖性。分类Gini协方差值为零意味着数值变量与分类变量相互独立。我们提出了一种基于分类Gini协方差的非参数检验方法，用于检验数值变量与分类变量之间的独立性。利用U-统计量理论构建检验统计量并研究其性质。该检验具有渐近正态分布。由于基于正态分布的检验实施困难，我们开发了一种刀切经验似然（JEL）比率检验用于独立性检验。通过大量蒙特卡洛模拟研究验证了所提JEL检验的性能，并利用实际数据集说明了检验流程。