Jackknife empirical likelihood inference for the Pietra ratio

The Pietra ratio (Pietra index) is also known as the Robin Hood index or Schutz coefficient (Ricci–Schutz index). It is a measure of statistical heterogeneity in positive random variables. In this paper, we propose the jackknife empirical likelihood (JEL), the adjusted JEL, the extended JEL, and the...

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Bibliographic Details
Published in:Computational statistics & data analysis 2020-12, Vol.152, p.107049, Article 107049
Main Authors: Zhao, Yichuan, Su, Yueju, Yang, Hanfang
Format: Article
Language:English
Subjects:
Adjusted jackknife empirical likelihood
Balanced jackknife empirical likelihood
Bootstrap method
Extended jackknife empirical likelihood
Jackknife empirical likelihood
Pietra index
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Summary:The Pietra ratio (Pietra index) is also known as the Robin Hood index or Schutz coefficient (Ricci–Schutz index). It is a measure of statistical heterogeneity in positive random variables. In this paper, we propose the jackknife empirical likelihood (JEL), the adjusted JEL, the extended JEL, and the balanced adjusted JEL method, for interval estimation of the Pietra ratio. We compare the performance of the proposed methods with the normal approximation (NA), bootstrap based methods and NA jackknife method. Simulation results indicate that under both symmetric and skewed distributions, the extended JEL method gives the best performance in terms of coverage probability. We illustrate the proposed methods by applying our methods to investigate the income data from the 2013 Current Population Survey conducted by the US Census Bureau.
ISSN:0167-9473
1872-7352
DOI:10.1016/j.csda.2020.107049