Non-smooth Empirical Likelihood Inference For Low-income Proportion

Low-income proportion is an important index used to describe the inequality of income distribution recognized by all around the world.It is often used to evaluate the human society economy and poverty.Low-income problems affect the development and progress of society,so the accurate estimation of this proportion is a great significance for the government to formulate policies.This paper mainly studies the non-smooth empirical likelihood inference of low-income proportion.Under simple random sampling and stratified random sampling,the limit distributions of the logarithmic empirical likelihood ratio of the low-income proportion are given,and obtained the following results:1.Under the simple random sampling,we proved that the limit distribution of logarithmic empirical likelihood ratio of low-income proportion is the standard Chi-square distribution.The method in this paper is compared and analyzed with other existing methods,which verifies the effectiveness of the method in this paper.2.Under the stratified random sampling,we proved that the limit distribution of the logarithmic empirical likelihood ratio of low-income proportion is a chi-square distribution with coefficients(coefficient associated with the sample size of each layer and the total sample amount),and had carried on the simulation data.