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Influence function-based empirical likelihood and generalized confidence intervals for the Lorenz curve

Author

Listed:
  • Yuyin Shi

    (Georgia State University)

  • Bing Liu

    (Georgia State University)

  • Gengsheng Qin

    (Georgia State University)

Abstract

This paper aims to solve confidence interval estimation problems for the Lorenz curve. First, we propose new nonparametric confidence intervals using the influence function-based empirical likelihood method. We show that the limiting distributions of the empirical log-likelihood ratio statistics for the Lorenz ordinates are standard chi-square distributions. We also develop “exact” parametric intervals for the Lorenz ordinate based on generalized pivotal quantities when the underlying income distribution is a Pareto distribution or a Lognormal distribution. Extensive simulation studies are conducted to evaluate the finite sample performances of the proposed methods. Finally, we apply our methods to a real income dataset.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stmapp:v:29:y:2020:i:3:d:10.1007_s10260-019-00482-w
    DOI: 10.1007/s10260-019-00482-w
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    References listed on IDEAS

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