Mathematics – Statistics Theory
Scientific paper
2005-04-25
Annals of Statistics 2005, Vol. 33, No. 1, 284-306
Mathematics
Statistics Theory
Published at http://dx.doi.org/10.1214/009053604000000959 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst
Scientific paper
10.1214/009053604000000959
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.
Hall Peter
Kang Kee-Hoon
No associations
LandOfFree
Bandwidth choice for nonparametric classification does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Bandwidth choice for nonparametric classification, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bandwidth choice for nonparametric classification will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-468932