On optimal data-based bandwidth selection in Kernel density estimation

Peter Hall; Simon J. Sheather; M. C. Jones; J. S. Marron

doi:10.1093/biomet/78.2.263

On optimal data-based bandwidth selection in Kernel density estimation

Peter Hall, Simon J. Sheather, M. C. Jones, J. S. Marron

Research output: Contribution to journal › Article › peer-review

189 Scopus citations

Abstract

A bandwidth selection method is proposed for Kernel density estimation. This is based on the straightforward idea of plugging estimates into the usual asymptotic representation for the optimal bandwidth, but with two important modifications. The result is a bandwidth selector with the, by nonparametric standards, extremely fast asymptotic rate of convergence of n^-2-Jan where n ↑ ∞ denotes sample size. Comparison is given to other bandwidth selection methods, and small sample impact is investigated.

Original language	English
Pages (from-to)	263-269
Number of pages	7
Journal	Biometrika
Volume	78
Issue number	2
DOIs	https://doi.org/10.1093/biomet/78.2.263
State	Published - Jun 1991

Bibliographical note

Funding Information:
M. C. Jones was supported by a Mathematical Sciences Research Centre Visiting Fellowship at the Australian National University. J. S. Marron was supported by the National Science Foundation.

Keywords

Adaptive procedure
Convergence rate
Functional estimation
Mean integrated squared error
Smoothing parameter
Taylor expansion
Window width

ASJC Scopus subject areas

Statistics and Probability
General Mathematics
Agricultural and Biological Sciences (miscellaneous)
General Agricultural and Biological Sciences
Statistics, Probability and Uncertainty
Applied Mathematics

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10.1093/biomet/78.2.263

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title = "On optimal data-based bandwidth selection in Kernel density estimation",

abstract = "A bandwidth selection method is proposed for Kernel density estimation. This is based on the straightforward idea of plugging estimates into the usual asymptotic representation for the optimal bandwidth, but with two important modifications. The result is a bandwidth selector with the, by nonparametric standards, extremely fast asymptotic rate of convergence of n-2-Jan where n ↑ ∞ denotes sample size. Comparison is given to other bandwidth selection methods, and small sample impact is investigated.",

keywords = "Adaptive procedure, Convergence rate, Functional estimation, Mean integrated squared error, Smoothing parameter, Taylor expansion, Window width",

author = "Peter Hall and Sheather, {Simon J.} and Jones, {M. C.} and Marron, {J. S.}",

note = "Funding Information: M. C. Jones was supported by a Mathematical Sciences Research Centre Visiting Fellowship at the Australian National University. J. S. Marron was supported by the National Science Foundation.",

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AU - Sheather, Simon J.

AU - Jones, M. C.

AU - Marron, J. S.

N1 - Funding Information: M. C. Jones was supported by a Mathematical Sciences Research Centre Visiting Fellowship at the Australian National University. J. S. Marron was supported by the National Science Foundation.

PY - 1991/6

Y1 - 1991/6

N2 - A bandwidth selection method is proposed for Kernel density estimation. This is based on the straightforward idea of plugging estimates into the usual asymptotic representation for the optimal bandwidth, but with two important modifications. The result is a bandwidth selector with the, by nonparametric standards, extremely fast asymptotic rate of convergence of n-2-Jan where n ↑ ∞ denotes sample size. Comparison is given to other bandwidth selection methods, and small sample impact is investigated.

AB - A bandwidth selection method is proposed for Kernel density estimation. This is based on the straightforward idea of plugging estimates into the usual asymptotic representation for the optimal bandwidth, but with two important modifications. The result is a bandwidth selector with the, by nonparametric standards, extremely fast asymptotic rate of convergence of n-2-Jan where n ↑ ∞ denotes sample size. Comparison is given to other bandwidth selection methods, and small sample impact is investigated.

KW - Adaptive procedure

KW - Convergence rate

KW - Functional estimation

KW - Mean integrated squared error

KW - Smoothing parameter

KW - Taylor expansion

KW - Window width

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EP - 269

JO - Biometrika

JF - Biometrika

IS - 2

ER -

On optimal data-based bandwidth selection in Kernel density estimation

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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