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Prospects for automatic bandwidth selection in extensions to basic kernel density estimation

Jones, M. C. (1991). Prospects for automatic bandwidth selection in extensions to basic kernel density estimation. In: Roussas, G. G. ed. Nonparametric Functional Estimation and Related Topics. NATO Science Series C (335). Dordrecht, Netherlands: Kluwer, pp. 241–249.

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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.

Item Type: Book Chapter
Copyright Holders: 1991 Kluwer Academic Publishers
ISBN: 0-7923-1226-0, 978-0-7923-1226-0
Extra Information: Proceedings of the NATO Advanced Study Institute, Spetses, Greece, July 29-August 10, 1990
Keywords: adaptive selection; convergence rates; cross-validation; estimating derivatives; functional estimation; higher order kernels; multivariate estimation; smoothing
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Mathematics, Computing and Technology
Item ID: 28309
Depositing User: Sarah Frain
Date Deposited: 09 Mar 2011 15:57
Last Modified: 18 Jan 2016 10:06
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