AISM 52, 612-629

## 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 $Y=X+\epsilon$ with $\epsilon$ 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.

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