Boundary Bias Correction for Nonparametric Deconvolution

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 + with 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.