BOUNDARY BIAS CORRECTION FOR NONPARAMETRIC DECONVOLUTION

SHUNPU ZHANG AND ROHANA J. KARUNAMUNI

Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1

(Received September 10, 1997; revised February 22, 1999)

Abstract. In this paper we consider the deconvolution problem in nonparametric density estimation. That is, one wishes to estimate the unknown density of a random variable X, say f_{X}, based on the observed variables Y ’s, where Y = X + ϵ with ϵ being the error. Previous results on this problem have considered the estimation of f_{X} at interior points. Here we study the deconvolution problem for boundary points. A kernel-type estimator is proposed, and its mean squared error properties, including the rates of convergence, are investigated for supersmooth and ordinary smooth error distributions. Results of a simulation study are also presented.

Key words and phrases: Deconvolution, density estimation, boundary effects, bandwidth variation.