  The Gini correlation plays an important role in measuring dependence of
random variables with heavy tailed distributions, whose properties are a
mixture of Pearson's and Spearman's correlations. Due to the structure of this
dependence measure, there are two Gini correlations between each pair of random
variables, which are not equal in general. Both the Gini correlation and the
equality of the two Gini correlations play important roles in Economics. In the
literature, there are limited papers focusing on the inference of the Gini
correlations and their equality testing. In this paper, we develop the
jackknife empirical likelihood (JEL) approach for the single Gini correlation,
for testing the equality of the two Gini correlations, and for the Gini
correlations' differences of two independent samples. The standard limiting
chi-square distributions of those jackknife empirical likelihood ratio
statistics are established and used to construct confidence intervals,
rejection regions, and to calculate $p$-values of the tests. Simulation studies
show that our methods are competitive to existing methods in terms of coverage
accuracy and shortness of confidence intervals, as well as in terms of power of
the tests. The proposed methods are illustrated in an application on a real
data set from UCI Machine Learning Repository.
