Non-parametric inferences for the generalized Lorenz curve

Abstract

In this paper, we discuss the empirical likelihood-based inferences for the generalized Lorenz (GL) curve. In the settings of simple random sampling, strati ed random sampling and cluster random sampling, it is shown that the limiting distributions of the empirical likelihood ratio statistics for the GL ordinate are the scaled χ² distributions with one degree of freedom. We also derive the limiting processes of the associated empirical likelihood-based GL processes. Various con dence intervals for the GL ordinate are proposed based on bootstrap method and the newly developed empirical likelihood theory. Extensive simulation studies are conducted to compare the relative performances of various con dence intervals for GL ordinates in terms of coverage probability and average interval length. The nite sample performances of the empirical likelihood- based con dence bands are also illustrated in simulation studies. Finally, a real example is used to illustrate the application of the recommended intervals.