Jones, M. C. and Kappenman, R. F.
(1991).
*Scandinavian Journal of Statistics*, 19(4) pp. 337–349.

URL: | http://www.jstor.org/stable/4616251 |
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## Abstract

A class of data-based bandwidth selection procedures for kernel density estimation is investigated. These procedures yield bandwidth estimates ĥ which have a (poor) relative error rate of convergence to h_{0}, the bandwidth which minimises mean integrated squared error, of order n^{-1/10} as n → ∞, where n is the sample size. Various members of this class are identified--some are new, but they include the well-known least squares cross-validation--and the unified treatment they receive is novel. Relative error rate of convergence of these ĥ’s to ĥ_{0} the bandwidth which minimises integrated squared error, is also examined. For this criterion, an n^{-1/10} convergence rate is best possible, and these ĥ's still achieve it. Our treatment of the latter problem has the important spinoff of helping clarify the role of methods which are better estimates of h_{0} (for which convergence rates as good as n^{-1/2} can be attained) in estimating ĥ_{0}. Constant multipliers of n-1/10 are derived throughout and these provide theoretical rankings of methods within the class. A small simulation study provides information about which comparisons are of real practical consequence. An important conclusion is that methods that are good at estimating ĥ_{0} are likely to be as good as any at estimating ĥ_{0}too.

Item Type: | Journal Article |
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Copyright Holders: | 1991 Board of the Foundation of the Scandinavian Journal of Statistics |

ISSN: | 0303-6898 |

Keywords: | adaptive procedure; convergence rate; integrated squared error; mean integrated; squared error; smoothing parameter; Taylor expansion; window width |

Academic Unit/Department: | Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics Faculty of Science, Technology, Engineering and Mathematics (STEM) |

Item ID: | 28312 |

Depositing User: | Sarah Frain |

Date Deposited: | 17 Mar 2011 14:25 |

Last Modified: | 02 Aug 2016 14:00 |

URI: | http://oro.open.ac.uk/id/eprint/28312 |

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