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

Yuyin Shi, Bing Liu and Gengsheng Qin ()
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Yuyin Shi: Georgia State University
Bing Liu: Georgia State University
Gengsheng Qin: Georgia State University

Statistical Methods & Applications, 2020, vol. 29, issue 3, No 1, 427-446

Abstract: 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.

Keywords: Empirical likelihood; Influence function; Generalized pivotal quantities; The Lorenz curve (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10260-019-00482-w

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