Boundary bias correction for nonparametric deconvolution

Shunpu Zhang, Rohana J. Karunamuni

Research output: Contribution to journalArticle

14 Scopus citations

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 fx, based on the observed variables Y's, where Y = X + ∈ with ∈ being the error. Previous results on this problem have considered the estimation of fx 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.

Original languageEnglish (US)
Pages (from-to)612-629
Number of pages18
JournalAnnals of the Institute of Statistical Mathematics
Volume52
Issue number4
DOIs
StatePublished - 2000

Keywords

  • Band-width variation
  • Boundary effects
  • Deconvolution
  • Density estimation

ASJC Scopus subject areas

  • Statistics and Probability

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