An effective bandwidth selector for local least squares regression

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

Research output: Contribution to journalArticlepeer-review

614 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 languageEnglish
Pages (from-to)1257-1270
Number of pages14
JournalJournal of the American Statistical Association
Volume90
Issue number432
DOIs
StatePublished - 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.

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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