On the estimation of the Lorenz curve under complex sampling designs
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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) Hájek 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.
KeywordsConcentration Resampling Bootstrap Finite population Superpopulation
Funding was provided by Sapienza Università di Roma (C26A144TFX - Nuove metodologie di ricampionamento per indagini complesse con applicazioni alla stima di misure di disuguaglianza; C26A15W8EK - Un nuovo approccio all’imputazione singola e multipla).
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