Bootstrap bandwidth selection in kernel density estimation from a contaminated sample

A Delaigle, I Gijbels

Research output: Contribution to journalArticle (Academic Journal)

53 Citations (Scopus)

Abstract

In this paper we consider kernel estimation of a density when the data are contaminated by random noise. More specifically we deal with the problem of how to choose the bandwidth parameter in practice. A theoretical optimal bandwidth is defined as the minimizer of the mean integrated squared error. We propose a bootstrap procedure to estimate this optimal bandwidth, and show its consistency. These results remain valid for the case of no measurement error, and hence also summarize part of the theory of bootstrap bandwidth selection in ordinary kernel density estimation. The finite sample performance of the proposed bootstrap selection procedure is demonstrated with a simulation study. An application to a real data example illustrates the use of the method.
Translated title of the contributionBootstrap bandwidth selection in kernel density estimation from a contaminated sample
Original languageEnglish
Pages (from-to)19 - 47
JournalAnnals of the Institute of Statistical Mathematics
Volume56 (1)
Publication statusPublished - Mar 2004

Bibliographical note

Publisher: Kluwer Academic Publ
Other identifier: IDS number 812NR

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