Summary
This paper provides a simulation study of several popular bandwidth selectors for local linear regression. The study also includes two new selectors which couple the non-asymptotic plug-in and the unbiased risk estimation techniques. These two new selectors are simple to describe, easy to implement and performed very well in our simulation study.








Similar content being viewed by others
Change history
11 September 2000
Due to a mix up a few lines of authors’ working notes were included in the article (page 530). These lines should be ignored and the remainder of the article is the correct final version.
References
Chiu, S.-T. (1991), ‘Some stabilized bandwidth selectors for nonparametric regression’, The Annals of Statistics 19, 1528–1546.
Chiu, S.-T. (1992), ‘An automatic bandwidth selector for kernel density estimation’, Biometrika 79, 771–782.
Chiu, S.-T. (1996), ‘A comparative review of bandwidth selection for kernel density estimation’, Statistica Sinica 6, 129–145.
Efron, B. & Tibshirani, R. J. (1993), An Introduction to the Bootstrap, Chapman and Hall, New York.
Fan, J. & Gijbels, I. (1995), ‘Data-driven bandwidth selection in local polynomial fitting: variable bandwidth and spatial adaptation’, Journal of the Royal Statistical Society Series B 57, 371–394.
Fan, J. & Gijbels, I. (1996), Local Polynomial Modelling and Its Applications, Chapman and Hall, London.
Gasser, T. & Müller, H. G. (1984), ‘Estimating regression functions and their derivatives by the kernel method’, Scandinavian Journal of Statistics 11, 171–185.
Gasser, T., Kneip, A. & Köhler, W. (1991), ‘A flexible and fast method for automatic smoothing’, Journal of the American Statistical Association 86, 643–652.
Hall, P. & Turlach, B. A. (1997), ‘Interpolation methods for adapting to sparse design in nonparametric regression’, Journal of the American Statistical Association 92, 466–476.
Hall, P., Marron, J. S. & Park, B. U. (1992), ‘Smoothed cross-validation’, Probability Theory and Related Fields 92, 1–20.
Hastie, T. & Loader, C. (1993), ‘Local regression: automatic kernel carpentry (with discussion)’, Statistical Sciences 8, 120–143.
Härdle, W., Hall, P. & Marron, J. S. (1992), ‘Regression smoothing parameters that are not far from their optimum’, Journal of the American Statistical Association 87, 227–233.
Jones, M. C. (1991), ‘The roles of ISE and MISE in density estimation’, Statistics and Probability Letters 12, 51–56.
Ruppert, D., Sheather, S. J. & Wand, M. P. (1995), ‘An effective bandwidth selector for local least squares regression’, Journal of the American Statistical Association 90, 1257–1270.
Wand, M. & Gutierrez, R. G. (1997), ‘Exact risk approaches to smoothing parameter selection’, Journal of Nonparametric Statistics 8, 337–354.
Wand, M. P. & Jones, M. C. (1995), Kernel Smoothing, Chapman and Hall, London.
Acknowledgment
Most of the work was done while the first author was with the Department of Statistics, Macquarie University. The authors thank Steve Marron, three anonymous referees and an associate editor for many helpful comments, and Matt Wand for providing a preprint of Wand & Gutierrez (1997). The work was partially supported by an Australian Research Council grant. This document was prepared using computer facilities supported in part by National Science Foundation Grant DMS 89-05292 awarded to the Department of Statistics at The University of Chicago, and by The University of Chicago Block Fund.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lee, T.C.M., Solo, V. Bandwidth selection for local linear regression: A simulation study. Computational Statistics 14, 515–532 (1999). https://doi.org/10.1007/s001800050029
Published:
Issue Date:
DOI: https://doi.org/10.1007/s001800050029