IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v65y2013i1p1-21.html
   My bibliography  Save this article

Empirical likelihood-based inferences for the Lorenz curve

Author

Listed:
  • Gengsheng Qin
  • Baoying Yang
  • Nelly Belinga-Hall

Abstract

In this paper, we discuss empirical likelihood-based inferences for the Lorenz curve. The profile empirical likelihood ratio statistics for the Lorenz ordinate are defined under the simple random sampling and the stratified random sampling designs. It is shown that the limiting distributions of the profile empirical likelihood ratio statistics are scaled Chi-square distributions with one degree of freedom. We also derive the limiting processes of the associated empirical likelihood-based Lorenz processes. Hybrid bootstrap and empirical likelihood intervals for the Lorenz ordinate are proposed based on the newly developed empirical likelihood theory. Extensive simulation studies are conducted to compare the relative performances of various confidence intervals for Lorenz ordinates in terms of coverage probability and average interval length. The finite sample performances of the empirical likelihood-based confidence bands are also illustrated in simulation studies. Finally, a real example is used to illustrate the application of the recommended intervals. Copyright The Institute of Statistical Mathematics, Tokyo 2013

Suggested Citation

  • Gengsheng Qin & Baoying Yang & Nelly Belinga-Hall, 2013. "Empirical likelihood-based inferences for the Lorenz curve," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(1), pages 1-21, February.
    • Handle: RePEc:spr:aistmt:v:65:y:2013:i:1:p:1-21
    DOI: 10.1007/s10463-012-0355-z
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10463-012-0355-z
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10463-012-0355-z?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. Chen S.X. & Leung D.H.Y. & Qin J., 2003. "Information Recovery in a Study With Surrogate Endpoints," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 1052-1062, January.
    2. Buhong Zheng, 2002. "Testing Lorenz Curves with Non-Simple Random Samples," Econometrica, Econometric Society, vol. 70(3), pages 1235-1243, May.
    3. Chen, Song Xi & Qin, Jing, 2003. "Empirical likelihood-based confidence intervals for data with possible zero observations," Statistics & Probability Letters, Elsevier, vol. 65(1), pages 29-37, October.
    4. Gastwirth, Joseph L, 1971. "A General Definition of the Lorenz Curve," Econometrica, Econometric Society, vol. 39(6), pages 1037-1039, November.
    5. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
    6. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    7. Doiron, Denise J & Barrett, Garry F, 1996. "Inequality in Male and Female Earnings: The Role of Hours and Wages," The Review of Economics and Statistics, MIT Press, vol. 78(3), pages 410-420, August.
    8. Charles M. Beach & Russell Davidson, 1983. "Distribution-Free Statistical Inference with Lorenz Curves and Income Shares," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(4), pages 723-735.
    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. Suthakaran Ratnasingam & Spencer Wallace & Imran Amani & Jade Romero, 2024. "Nonparametric confidence intervals for generalized Lorenz curve using modified empirical likelihood," Computational Statistics, Springer, vol. 39(6), pages 3073-3090, September.
    2. Yuyin Shi & Bing Liu & Gengsheng Qin, 2020. "Influence function-based empirical likelihood and generalized confidence intervals for the Lorenz curve," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(3), pages 427-446, September.

    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. 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.
    2. ANDREOLI Francesco & HAVNES Tarjei & LEFRANC Arnaud, 2014. "Equalization of opportunity: Definitions, implementable conditions and application to early-childhood policy evaluation," LISER Working Paper Series 2014-12, Luxembourg Institute of Socio-Economic Research (LISER).
    3. Sarabia Alegría, J.M & Pascual Sáez, Marta, 2001. "Rankings de distribuciones de renta basados en curvas de Lorenz ordenadas: un estudio empírico1," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 19, pages 151-169, Diciembre.
    4. Francesco Andreoli & Tarjei Havnes & Arnaud Lefranc, 2019. "Robust Inequality of Opportunity Comparisons: Theory and Application to Early Childhood Policy Evaluation," The Review of Economics and Statistics, MIT Press, vol. 101(2), pages 355-369, May.
    5. Yuyin Shi & Bing Liu & Gengsheng Qin, 2020. "Influence function-based empirical likelihood and generalized confidence intervals for the Lorenz curve," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(3), pages 427-446, September.
    6. Francesco Andreoli, 2018. "Robust Inference for Inverse Stochastic Dominance," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(1), pages 146-159, January.
    7. Daniel Sotelsek-Salem & Ismael Ahamdanech-Zarco & John Bishop, 2012. "Dominance testing for ‘pro-poor’ growth with an application to European growth," Empirical Economics, Springer, vol. 43(2), pages 723-739, October.
    8. Chiou, Jong-Rong, 1996. "A dominance evaluation of Taiwan's official income distribution statistics, 1976-1992," China Economic Review, Elsevier, vol. 7(1), pages 57-75.
    9. Francesco Andreoli & Claudio Zoli, 2020. "From unidimensional to multidimensional inequality: a review," METRON, Springer;Sapienza Università di Roma, vol. 78(1), pages 5-42, April.
    10. Gravel, Nicolas & Moyes, Patrick, 2012. "Ethically robust comparisons of bidimensional distributions with an ordinal attribute," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1384-1426.
    11. Nicolas Gravel & Patrick Moyes, 2006. "Ethically Robust Comparisons of Distributions of Two Individual Attributes," IDEP Working Papers 0605, Institut d'economie publique (IDEP), Marseille, France, revised Aug 2006.
    12. Claudio Zoli, 2002. "Inverse stochastic dominance, inequality measurement and Gini indices," Journal of Economics, Springer, vol. 77(1), pages 119-161, December.
    13. Suthakaran Ratnasingam & Spencer Wallace & Imran Amani & Jade Romero, 2024. "Nonparametric confidence intervals for generalized Lorenz curve using modified empirical likelihood," Computational Statistics, Springer, vol. 39(6), pages 3073-3090, September.
    14. Giovanni Giorgi, 2014. "A couple of good reasons to translate papers of the Italian statistical tradition," METRON, Springer;Sapienza Università di Roma, vol. 72(1), pages 1-3, April.
    15. Beach, Charles M., 1979. "Model-Free Statistical Inference with Lorenz Curves, Income Shares, and Gini Coefficients," Queen's Institute for Economic Research Discussion Papers 275154, Queen's University - Department of Economics.
    16. Duclos, J.Y. & Tabi, M., 1996. "Linear Inequality Measures and the Redistribution of Income," Papers 9613, Laval - Recherche en Politique Economique.
    17. Louis Mesnard, 2022. "About some difficulties with the functional forms of Lorenz curves," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 20(4), pages 939-950, December.
    18. Patrick Moyes, 2007. "An extended Gini approach to inequality measurement," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 5(3), pages 279-303, December.
    19. Francesco Andreoli & Arnaud Lefranc, 2013. "Equalization of opportunity: Definitions and implementable conditions," Working Papers 310, ECINEQ, Society for the Study of Economic Inequality.
    20. Sarabia, J. -M. & Castillo, Enrique & Slottje, Daniel J., 1999. "An ordered family of Lorenz curves," Journal of Econometrics, Elsevier, vol. 91(1), pages 43-60, July.

    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:aistmt:v:65:y:2013:i:1:p:1-21. 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.