Reduce the computation in jackknife empirical likelihood for comparing two correlated Gini indices

The Gini index has been widely used as a measure of income (or wealth) inequality in social sciences. To construct a confidence interval for the difference of two Gini indices from the paired samples, Wang and Zhao ['Jackknife Empirical Likelihood for Comparing Two Gini Indices', The Canadian Journal of Statistics, 44(1), 102-119] used a profile jackknife empirical likelihood. However, the computing cost with the profile empirical likelihood could be very expensive. In this paper, we propose an alternative approach of the jackknife empirical likelihood method to reduce the computational cost. We also investigate the adjusted jackknife empirical likelihood and the bootstrap-calibrated jackknife empirical likelihood to improve coverage accuracy for small samples. Simulations show that the proposed methods perform better than Wang and Zhao's methods in terms of coverage accuracy and computational time. Real data applications demonstrate that the proposed methods work very well in practice.