Influence function-based empirical likelihood and generalized confidence intervals for the Lorenz curve
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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.
KeywordsEmpirical likelihood Influence function Generalized pivotal quantities The Lorenz curve
The authors are thankful to the anonymous referees for their helpful suggestions and comments.
- Binder DA, Kovacevic MS (1995) Estimating some measures of income inequality from survey data: an application of the estimation equation approach. Surv Methodol 21:137–145Google Scholar
- Clementi F, Gallegati M (2005) Pareto’s law of income distribution: evidence for Germany, the United Kingdom, and the United States. In: Chatterjee A, Yarlagadda S, Chakrabarti BK (eds) Econophysics of wealth distributions. Springer, MilanGoogle Scholar
- Graf E, Tille Y (2014) Variance estimation using linearization for poverty and social exclusion Indicators. Surv Methodol 40:61–79Google Scholar
- Kovacevic MS, Yung W (1997) Variance estimation for measures of income inequality and polarization—an empirical study. Surv Methodol 23:41–52Google Scholar
- Osier G (2009) Variance estimation for complex indicators of poverty and inequality using linearization techniques. Surv Res Methods 3:167–195Google Scholar
- Panel Study of Income Dynamics, public use dataset (2017) Produced and distributed by the Institute for Social Research, University of Michigan, Ann Arbor, MIGoogle Scholar
- Pareto V, Page AN (1971) Translation of Manuale di economia politica (“Manual of political economy”), A.M. Kelley, ISBN 978-0-678-00881-2Google Scholar
- Weeks J (2007) Inequality trends in some developed OECD countries. United Nations DESA working paper, 6Google Scholar