In this study, I propose a new estimator for the DER index that is a general measure of polarization introduced by Duclos et al.(2004). The existing estimators for the DER index are based on the empirical distribution function and a Rosenblatt-Parzen density estimator. The empirical distribution function, however, suffers from lack of smoothness. Hence, I suggest new estimators for the DER index using a new class of nonparametric kernel density estimators provided by Mynbaev and Martins-Filho(2010). I show that my estimators for polarization measure are consistent and establish asymptotic normality with a rate of convergence for the distribution of . A small Monte Carlo study reveals that my estimator performs well relative to the existing estimator for the DER index in terms of bias and mean squared error.
키워드 : Polarization Measure, DER Index, Nonparametric Density