Smoothed Jackknife Empirical Likelihood Inference For The Difference Of Lorenz Curves

The Lorenz curve,a popular measure of inequality,has been widely used in economic analysis and social sciences.In this paper,we are concerned with comparing two Lorenz curves.First,we introduce the background and the latest research of the Lorenz curve.Then we describe the method of this paper.We use the kernel function to smooth the difference between two Lorentz curves,and use the jackknife method to make its constraints linear.The traditional empirical likelihood method is used to calculate the point estimate of this difference.It can be proved that the statistic constructed by the smoothed jackknife empirical likelihood method will converge to the standard chi-squared distribution.By this good property,we can estimate the confidence interval of the difference between two Lorentz curves,so a simulation experiment on the lognormal income distribution is carried out.The simulation results contain the coverage probabilities and lengths of the confidence interval about the true value.At the same confidence level,the confidence interval of the smoothed jackknife empirical method is shorter than that of the traditional normal method.Simulation studies and real data analysis are also conducted,and show encouraging finite sample performance.