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.
Pier Luigi Conti, ., DI IORIO, A., Alessio, G., Marella, D., Vicard, P., Vitale, V. (2019). On the estimation of the Lorenz curve under complex sampling designs. STATISTICAL METHODS & APPLICATIONS, 29, 1-24 [https://doi.org/10.1007/s10260-019-00478-6].
On the estimation of the Lorenz curve under complex sampling designs
DI IORIO, ALBERTO;Daniela Marella;Paola Vicard;Vincenzina Vitale
2019-01-01
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
