An effective bandwidth selector for local least squares regression

D. Ruppert; S. J. Sheather; M. P. Wand

doi:10.1080/01621459.1995.10476630

An effective bandwidth selector for local least squares regression

D. Ruppert, S. J. Sheather, M. P. Wand

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

619 Scopus citations

Abstract

Local least squares kernel regression provides an appealing solution to the nonparametric regression, or “scatterplot smoothing,” problem, as demonstrated by Fan, for example. The practical implementation of any scatterplot smoother is greatly enhanced by the availability of a reliable rule for automatic selection of the smoothing parameter. In this article we apply the ideas of plug-in bandwidth selection to develop strategies for choosing the smoothing parameter of local linear squares kernel estimators. Our results are applicable to odd-degree local polynomial fits and can be extended to other settings, such as derivative estimation and multiple nonparametric regression. An implementation in the important case of local linear fits with univariate predictors is shown to perform well in practice. A by-product of our work is the development of a class of nonparametric variance estimators, based on local least squares ideas, and plug-in rules for their implementation.

Original language	English
Pages (from-to)	1257-1270
Number of pages	14
Journal	Journal of the American Statistical Association
Volume	90
Issue number	432
DOIs	https://doi.org/10.1080/01621459.1995.10476630
State	Published - Dec 1995

Bibliographical note

Funding Information:
D. Ruppert is Professor, School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY 14853. S. J. Sheather is Associate Professor and M. P. Wand is Senior Lecturer, Australian Graduate School of Management, University of New South Wales, Kensington, NSW 2033, Australia. This research was partially supported by National Science Foundation Grants DMS-9002791 and DMS-9306196, National Institute of General Medical Sciences Grant GM-39015, and a grant from the Australian Research Council. The authors are grateful to two referee’s and an associate editor for their helpful comments.

Funding

D. Ruppert is Professor, School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY 14853. S. J. Sheather is Associate Professor and M. P. Wand is Senior Lecturer, Australian Graduate School of Management, University of New South Wales, Kensington, NSW 2033, Australia. This research was partially supported by National Science Foundation Grants DMS-9002791 and DMS-9306196, National Institute of General Medical Sciences Grant GM-39015, and a grant from the Australian Research Council. The authors are grateful to two referee’s and an associate editor for their helpful comments.

Funders	Funder number
National Science Foundation (NSF)	DMS-9002791, DMS-9306196
National Institute of General Medical Sciences	GM-39015
Australian Research Council

Keywords

Boundary effects
Kernel estimator
Local polynomial fitting
Nonparametric regression
Pilot estimation
Variance estimation

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1080/01621459.1995.10476630

Cite this

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title = "An effective bandwidth selector for local least squares regression",

abstract = "Local least squares kernel regression provides an appealing solution to the nonparametric regression, or “scatterplot smoothing,” problem, as demonstrated by Fan, for example. The practical implementation of any scatterplot smoother is greatly enhanced by the availability of a reliable rule for automatic selection of the smoothing parameter. In this article we apply the ideas of plug-in bandwidth selection to develop strategies for choosing the smoothing parameter of local linear squares kernel estimators. Our results are applicable to odd-degree local polynomial fits and can be extended to other settings, such as derivative estimation and multiple nonparametric regression. An implementation in the important case of local linear fits with univariate predictors is shown to perform well in practice. A by-product of our work is the development of a class of nonparametric variance estimators, based on local least squares ideas, and plug-in rules for their implementation.",

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AB - Local least squares kernel regression provides an appealing solution to the nonparametric regression, or “scatterplot smoothing,” problem, as demonstrated by Fan, for example. The practical implementation of any scatterplot smoother is greatly enhanced by the availability of a reliable rule for automatic selection of the smoothing parameter. In this article we apply the ideas of plug-in bandwidth selection to develop strategies for choosing the smoothing parameter of local linear squares kernel estimators. Our results are applicable to odd-degree local polynomial fits and can be extended to other settings, such as derivative estimation and multiple nonparametric regression. An implementation in the important case of local linear fits with univariate predictors is shown to perform well in practice. A by-product of our work is the development of a class of nonparametric variance estimators, based on local least squares ideas, and plug-in rules for their implementation.

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An effective bandwidth selector for local least squares regression

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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