Nonparametric confidence intervals for generalized Lorenz curve using modified empirical likelihood

The Lorenz curve portrays income distribution inequality. In this article, we develop three modified empirical likelihood (EL) approaches, including adjusted empirical likelihood, transformed empirical likelihood, and transformed adjusted empirical likelihood, to construct confidence intervals for the generalized Lorenz ordinate. We demonstrate that the limiting distribution of the modified EL ratio statistics for the generalized Lorenz ordinate follows scaled Chi-Squared distributions with one degree of freedom. We compare the coverage probabilities and mean lengths of confidence intervals of the proposed methods with the traditional EL method through simulations under various scenarios. Finally, we illustrate the proposed methods using real data to construct confidence intervals.

Automated summary

This article introduces three modified empirical likelihood approaches to construct confidence intervals for the generalized Lorenz ordinate. The proposed methods are validated through simulation and real data.