Novel inferential methods proposed for Gini index


  • Author: Statistics Views, Dongliang Wang and Yichuan Zhao
  • Date: 02 February 2016

Wiley authors have released a paper which focuses on deriving the jackknife empirical likelihood for the difference of two Gini indices. For independent data they propose a novel U-statistic, which allows direct utilization of the jackknife empirical likelihood without involving a nuisance parameter. For paired data the authors established Wilks’ theorem for the profile likelihood after maximization over the nuisance parameter. Simulation studies show that their method is comparable to existing empirical likelihood methods in terms of coverage accuracy, but obtains much shorter intervals.

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The Gini index is one of the most widely used measure of income and wealth inequality, which can be generally used to measure the inequality among individual values of a specific population. The majority of statisticians’ attention has been given to obtain a reliable interval estimator for a single Gini index, which lays out a range of values that is supposed to cover the true Gini index at a desired probability level. The availability of statistical methods for comparing two Gini indices is somehow limited.

An article recently published in the Canadian Journal of Statistics addresses the inadequateness by proposing novel inferential methods for the difference of two Gini indices. The authors derive interval estimators towards extending the jackknife empirical likelihood, which is a combination of two classic nonparametric statistical methods: jackknife and empirical likelihood. These methods allow us to assess whether the Gini indices are different between two regions (independent data) or the Gini index changes over time (paired data). Simulation studies suggest that the proposed interval estimators from the jackknife empirical likelihood method are much more accurate than those derived by applying solely the empirical likelihood method. Thus the new interval estimators are more powerful to detect the significant difference of two Gini indices, while maintaining a satisfactory level of coverage probability.

Jackknife empirical likelihood for comparing two Gini indices

Dongliang Wang and Yichuan Zhao

Canadian Journal of Statistics

DOI: 10.1002/cjs.11275

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