Abstract
Recently, much progress has been made on understanding the bandwidth selection problem in kernel density estimation. Here, analogous questions are considered for extensions to the basic problem, namely, for estimating derivatives, using “better” kernel estimators, and for the multivariate case. In basic kernel density estimation, recent advances have resulted in considerable improvements being made over “moderate” methods such as least squares cross-validation. Here, it is argued that, in the first two extension cases, the performance of moderate methods deteriorates even more, so that the necessity for “improved” methods — and indeed their potential in theory if not necessarily in practice — is greatly increased. Rather extraordinary things happen, however, when higher dimensions are considered.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Chiu, S.-T. (1990) ‘Why bandwidth selectors tend to choose smaller bandwidths, and a remedy’, Biometrika 77, 222–226.
Hall, P. (1989a) ‘On bandwidth selection for variable bandwidth density estimation’, to appear.
Hall, P. (1989b) ‘On the bias of variable bandwidth curve estimators’, Technical Report CSTR-011-89, Statistics Research Section, Australian National University.
Hall, P. and Marron, J.S. (1987) ‘Estimation of integrated squared density derivatives’, Statist. Probab. Lett. 6, 109–115.
Hall, P., Sheather, S.J., Jones, M.C. and Marron, J.S. (1989) ‘On optimal data-based bandwidth selection in kernel density estimation’, to appear.
Jones, M.C. and Kappenman, R.F. (1989) ‘On a class of kernel density estimate bandwidth selectors’, to appear.
Jones, M.C. and Sheather, S.J. (1990) ‘Using non-stochastic terms to advantage in kernel-based estimation of integrated squared density derivatives’. Statist Probab. Lett., to appear.
Marron, J.S. (1986) “Will the art of smoothing ever become a science?”, Contemp. Math. 59, 169–178.
Marron, J.S. (this volume) ‘Root-n bandwidth selection’.
Park, B.U. and Marron, J.S. (1990) ‘Comparison of data-driven bandwidth selectors’, J. Amer. Statist. Assoc. 85, 66–72.
Sheather, S.J. and Jones, M.C. (1990) ‘A reliable data-based bandwidth selection method for kernel density estimation’, J. Roy. Statist. Soc. Ser. B, to appear.
Silverman, B.W. (1986) Density Estimation for Statistics and Data Analysis, Chapman and Hall, London.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Jones, M.C. (1991). Prospects for Automatic Bandwidth Selection in Extensions to Basic Kernel Density Estimation. In: Roussas, G. (eds) Nonparametric Functional Estimation and Related Topics. NATO ASI Series, vol 335. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3222-0_18
Download citation
DOI: https://doi.org/10.1007/978-94-011-3222-0_18
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5420-1
Online ISBN: 978-94-011-3222-0
eBook Packages: Springer Book Archive