On the estimation of the Lorenz curve under complex sampling designs

  • Pier Luigi ContiEmail author
  • Alberto Di Iorio
  • Alessio Guandalini
  • Daniela Marella
  • Paola Vicard
  • Vincenzina Vitale
Original Paper


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.


Concentration 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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Pier Luigi Conti
    • 1
    Email author
  • Alberto Di Iorio
    • 5
  • Alessio Guandalini
    • 2
  • Daniela Marella
    • 3
  • Paola Vicard
    • 4
  • Vincenzina Vitale
    • 6
  1. 1.Dipartimento di Scienze StatisticheSapienza Università di RomaRomeItaly
  2. 2.ISTATRomeItaly
  3. 3.Dipartimento di Scienze della FormazioneUniversità Roma TreRomeItaly
  4. 4.Dipartimento di EconomiaUniversità Roma TreRomeItaly
  5. 5.Banca D’ItaliaRomaItaly
  6. 6.Dipartimento di Scienze Sociali ed EconomicheSapienza Università di RomaRomaItaly

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