IDEAS home Printed from https://ideas.repec.org/a/spr/stmapp/v29y2020i1d10.1007_s10260-019-00478-6.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10260-019-00478-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10260-019-00478-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Giovanni Maria Giorgi & Chiara Gigliarano, 2017. "The Gini Concentration Index: A Review Of The Inference Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 31(4), pages 1130-1148, September.
    2. Garry F. Barrett & Stephen G. Donald & Debopam Bhattacharya, 2014. "Consistent Nonparametric Tests for Lorenz Dominance," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(1), pages 1-13, January.
    3. Buhong Zheng, 2002. "Testing Lorenz Curves with Non-Simple Random Samples," Econometrica, Econometric Society, vol. 70(3), pages 1235-1243, May.
    4. Gastwirth, Joseph L, 1972. "The Estimation of the Lorenz Curve and Gini Index," The Review of Economics and Statistics, MIT Press, vol. 54(3), pages 306-316, August.
    5. 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.
    6. Davidson, Russell, 2009. "Reliable inference for the Gini index," Journal of Econometrics, Elsevier, vol. 150(1), pages 30-40, May.
    7. Daniela Marella, 2018. "Pc Complex: Pc Algorithm For Complex Survey Data," Departmental Working Papers of Economics - University 'Roma Tre' 0240, Department of Economics - University Roma Tre.
    8. Pier Luigi Conti & Daniela Marella, 2015. "Inference for Quantiles of a Finite Population: Asymptotic versus Resampling Results," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 545-561, June.
    9. Bhattacharya, Debopam, 2007. "Inference on inequality from household survey data," Journal of Econometrics, Elsevier, vol. 137(2), pages 674-707, April.
    10. Anderson, Gordon, 1996. "Nonparametric Tests of Stochastic Dominance in Income Distributions," Econometrica, Econometric Society, vol. 64(5), pages 1183-1193, September.
    11. Bhattacharya, Debopam, 2005. "Asymptotic inference from multi-stage samples," Journal of Econometrics, Elsevier, vol. 126(1), pages 145-171, May.
    12. Matti Langel & Yves Tillé, 2013. "Variance estimation of the Gini index: revisiting a result several times published," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 176(2), pages 521-540, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bhargab Chattopadhyay & Shyamal Krishna De, 2016. "Estimation of Gini Index within Pre-Specified Error Bound," Econometrics, MDPI, vol. 4(3), pages 1-12, June.
    2. Frank A. Cowell & Emmanuel Flachaire, 2014. "Statistical Methods for Distributional Analysis," Working Papers halshs-01115996, HAL.
    3. Berger Yves G. & Balay İklim Gedik, 2020. "Confidence Intervals of Gini Coefficient Under Unequal Probability Sampling," Journal of Official Statistics, Sciendo, vol. 36(2), pages 237-249, June.
    4. Xiaofeng Lv & Gupeng Zhang & Guangyu Ren, 2017. "Gini index estimation for lifetime data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(2), pages 275-304, April.
    5. Zhao, Puying & Haziza, David & Wu, Changbao, 2020. "Survey weighted estimating equation inference with nuisance functionals," Journal of Econometrics, Elsevier, vol. 216(2), pages 516-536.
    6. Judith A. Clarke & Ahmed A. Hoque, 2014. "On Variance Estimation for a Gini Coefficient Estimator Obtained from Complex Survey Data," Econometrics Working Papers 1401, Department of Economics, University of Victoria.
    7. Jean-Marie Dufour & Emmanuel Flachaire & Lynda Khalaf, 2019. "Permutation Tests for Comparing Inequality Measures," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(3), pages 457-470, July.
    8. Judith Clarke & Nilanjana Roy, 2012. "On statistical inference for inequality measures calculated from complex survey data," Empirical Economics, Springer, vol. 43(2), pages 499-524, October.
    9. Christopher J. Bennett, 2013. "Inference For Dominance Relations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 54(4), pages 1309-1328, November.
    10. Silvia De Nicol`o & Maria Rosaria Ferrante & Silvia Pacei, 2021. "Mind the Income Gap: Bias Correction of Inequality Estimators in Small-Sized Samples," Papers 2107.08950, arXiv.org, revised May 2023.
    11. Amparo Ba'illo & Javier C'arcamo & Carlos Mora-Corral, 2024. "Tests for almost stochastic dominance," Papers 2403.15258, arXiv.org.
    12. Alessio Guandalini, 2022. "Things you should know about the Gini index," RIEDS - Rivista Italiana di Economia, Demografia e Statistica - The Italian Journal of Economic, Demographic and Statistical Studies, SIEDS Societa' Italiana di Economia Demografia e Statistica, vol. 76(4), pages 4-12, October-D.
    13. Amparo Ba'illo & Javier C'arcamo & Carlos Mora-Corral, 2021. "Extremal points of Lorenz curves and applications to inequality analysis," Papers 2103.03286, arXiv.org.
    14. Francesco Andreoli, 2018. "Robust Inference for Inverse Stochastic Dominance," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(1), pages 146-159, January.
    15. Encarnación Álvarez-Verdejo & Pablo J. Moya-Fernández & Juan F. Muñoz-Rosas, 2021. "Single Imputation Methods and Confidence Intervals for the Gini Index," Mathematics, MDPI, vol. 9(24), pages 1-20, December.
    16. Francesco Andreoli & Eugenio Peluso, 2016. "So close yet so unequal: Reconsidering spatial inequality in U.S. cities," Working Papers 21/2016, University of Verona, Department of Economics.
    17. Ziqing Dong & Yves Tillé & Giovanni M. Giorgi & Alessio Guandalini, 2021. "Linearization and variance estimation of the Bonferroni inequality index," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(3), pages 1008-1029, July.
    18. Karoly, Lynn & Schröder, Carsten, 2015. "Fast methods for jackknifing inequality indices," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 37(1), pages 125-138.
    19. Sudheesh K. Kattumannil & N. Sreelakshmi & N. Balakrishnan, 2022. "Non-Parametric Inference for Gini Covariance and its Variants," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 790-807, August.
    20. Barrett, Garry F. & Donald, Stephen G. & Hsu, Yu-Chin, 2016. "Consistent tests for poverty dominance relations," Journal of Econometrics, Elsevier, vol. 191(2), pages 360-373.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stmapp:v:29:y:2020:i:1:d:10.1007_s10260-019-00478-6. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.