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 + ∈ 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.
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Zhang, S., Karunamuni, R.J. Boundary Bias Correction for Nonparametric Deconvolution. Annals of the Institute of Statistical Mathematics 52, 612–629 (2000). https://doi.org/10.1023/A:1017564907869
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DOI: https://doi.org/10.1023/A:1017564907869