Smoothed Jackknife Empirical Likelihood Inferences for Lorenz Curves

• Activity Number: 662
• Type: Contributed
• Date/Time: Thursday, August 2, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Shan Luo*+ and Gengsheng Qin and Xin Huang
• Companies: Georgia State University and Georgia State University and Fred Hutchinson Cancer Research Center
• Keywords: Lorenz curve ; Empirical likelihood ; Jackknife ; Bootstrap ; Cross-validation ; Simple random sampling

Abstract

Lorenz curve is one of the most commonly used devices for describing the inequality of income distributions. Efficient inference methods for Lorenz curve, however, are still on demand due to the mathematical complexity and computational difficulty of the sampling distribution of the estimated Lorenz curve. In this paper, we propose a smoothed jackknife empirical likelihood method to construct confidence intervals for the Lorenz and the generalized Lorenz ordinates. It is shown that the Wilks' theorem for the proposed statistics still holds. Extensive simulation studies are conducted to compare the finite sample performance of the proposed method with other methods based on simple random samples. Finally, the proposed methods are illustrated with a real example.