On the estimation of the Lorenz curve under complex sampling designs

摘要

This paper focuses on the estimation of the concentration curve of a finite population, when data are collected according to a complex sampling design with different inclusion probabilities. A (design-based) Hajek type estimator for the Lorenz curve is proposed, and its asymptotic properties are studied. Then, a resampling scheme able to approximate the asymptotic law of the Lorenz curve estimator is constructed. Applications are given to the construction of (ⅰ) a confidence band for the Lorenz curve, (ⅱ) confidence intervals for the Gini concentration ratio, and (ⅲ) a test for Lorenz dominance. The merits of the proposed resampling procedure are evaluated through a simulation study.