Statistics and Its Interface

Volume 9 (2016)

Number 1

Kernel smoothing and jackknife empirical likelihood-based inferences for the generalized Lorenz curve

Pages: 99 – 112

DOI: http://dx.doi.org/10.4310/SII.2016.v9.n1.a10

Authors

Shan Luo (Department of Mathematics and Statistics, Georgia State University, Atlanta, Ga., U.S.A.)

Gengsheng Qin (Department of Mathematics and Statistics, Georgia State University, Atlanta, Ga., U.S.A.)

Abstract

Lorenz curve is one of the most commonly used devices for describing the inequality of income distributions. The generalized Lorenz curve is the Lorenz curve scaled by the mean of an income distribution and itself is an interesting object of study. In this paper, we define a smoothed estimator for the generalized Lorenz curve and propose a smoothed jackknife empirical likelihood method to construct confidence intervals for the generalized Lorenz curve. It is shown that the Wilks’ theorem still holds for the smoothed jackknife empirical likelihood. Extensive simulation studies are conducted to compare the finite sample performances of the proposed methods with other methods based on simple random samples. Finally, the proposed methods are illustrated with a real example.

Keywords

bootstrap, confidence interval, empirical likelihood, generalized Lorenz curve, jackknife

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