Empirical Bayes Nonparametric Kernel Density Estimation

Abstract

This manuscript proposes using empirical Bayes techniques on estimated density values from nonparametric kernels in attempts to exploit potential similarities among a set of unknown densities. Our asymptotic theory and simulation results suggest that the emipirical Bayes nonparamtetric kernel estimator may be a viable alternative to the standard kernel estimator when a set of possibly similar densities are being estimated. The strengths of the proposed estimator are (i) it allows all types of kernel estimators; and (ii) it does not require specification as to the degree or form of similarity.