Nonparametric Estimation of a Polarization Measure

Abstract

This paper develops methodology for nonparametric estimation of apolarization measure due to Anderson (2004) and Anderson, Ge, and Leo(2006) based on kernel estimation techniques. We give the asymptoticdistribution theory of our estimator, which in some cases is nonstandard dueto a boundary value problem. We also propose a method for conductinginference based on estimation of unknown quantities in the limitingdistribution and show that our method yields consistent inference in allcases we consider. We investigate the finite sample properties of ourmethods by simulation methods. We give an application to the study ofpolarization within China in recent years.Kernel Estimation, Inequality, Overlap coefficient,Poissonization