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On the estimation of the Lorenz curve under complex sampling designs

Author

Listed:
  • Pier Luigi Conti

    (Sapienza Università di Roma)

  • Alberto Iorio

    (Banca D’Italia)

  • Alessio Guandalini

    (ISTAT)

  • Daniela Marella

    (Università Roma Tre)

  • Paola Vicard

    (Università Roma Tre)

  • Vincenzina Vitale

    (Sapienza Università di Roma)

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.

Suggested Citation

  • Pier Luigi Conti & Alberto Iorio & Alessio Guandalini & Daniela Marella & Paola Vicard & Vincenzina Vitale, 2020. "On the estimation of the Lorenz curve under complex sampling designs," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(1), pages 1-24, March.
    • Handle: RePEc:spr:stmapp:v:29:y:2020:i:1:d:10.1007_s10260-019-00478-6
    DOI: 10.1007/s10260-019-00478-6
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    References listed on IDEAS

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    1. Antal, Erika & Tillé, Yves, 2011. "A Direct Bootstrap Method for Complex Sampling Designs From a Finite Population," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 534-543.
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    Cited by:

    1. Daniela Marella & Paola Vicard, 2022. "Bayesian network structural learning from complex survey data: a resampling based approach," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(4), pages 981-1013, October.

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