Bandwidth choice for nonparametric classification release_pjnwr64zr5cizko37gijn4abjy

by Peter Hall, Kee-Hoon Kang

Released as a report .

2005  

Abstract

It is shown that, for kernel-based classification with univariate distributions and two populations, optimal bandwidth choice has a dichotomous character. If the two densities cross at just one point, where their curvatures have the same signs, then minimum Bayes risk is achieved using bandwidths which are an order of magnitude larger than those which minimize pointwise estimation error. On the other hand, if the curvature signs are different, or if there are multiple crossing points, then bandwidths of conventional size are generally appropriate. The range of different modes of behavior is narrower in multivariate settings. There, the optimal size of bandwidth is generally the same as that which is appropriate for pointwise density estimation. These properties motivate empirical rules for bandwidth choice.
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Type  report
Stage   submitted
Date   2005-04-25
Version   v1
Language   en ?
Number  IMS-AOS-AOS303
arXiv  math/0504511v1
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