Nonparametric estimation and inference about the overlap of two distributions

Gordon Anderson, Oliver Linton, Yoon Jae Whang

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23 Citations (Scopus)

Abstract

This paper develops methodology for nonparametric estimation of a measure of the overlap of two distributions based on kernel estimation techniques. This quantity has been proposed as a measure of economic polarization between two groups, Anderson (2004) and Anderson et al. (2010). In ecology it has been used to measure the overlap of species. We give the asymptotic distribution theory of our estimator, which in some cases of practical relevance is nonstandard due to a boundary value problem. We also propose a method for conducting inference based on estimation of unknown quantities in the limiting distribution and show that our method yields consistent inference in all cases we consider. We investigate the finite sample properties of our methods by simulation methods. We give an application to the study of polarization within China in recent years using household survey data from two provinces taken in 1987 and 2001. We find a big increase in polarization between 1987 and 2001 according to monetary outcomes but less change in terms of living space.

Original languageEnglish
Pages (from-to)1-23
Number of pages23
JournalJournal of Econometrics
Volume171
Issue number1
DOIs
Publication statusPublished - Nov 2012
Externally publishedYes

Keywords

  • Inequality
  • Kernel estimation
  • Overlap coefficient
  • Poissonization
  • Total variation

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