Jackknife empirical likelihood inference for the Pietra ratio

Abstract

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.