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December 2013 Unexpected properties of bandwidth choice when smoothing discrete data for constructing a functional data classifier
Raymond J. Carroll, Aurore Delaigle, Peter Hall
Ann. Statist. 41(6): 2739-2767 (December 2013). DOI: 10.1214/13-AOS1158

Abstract

The data functions that are studied in the course of functional data analysis are assembled from discrete data, and the level of smoothing that is used is generally that which is appropriate for accurate approximation of the conceptually smooth functions that were not actually observed. Existing literature shows that this approach is effective, and even optimal, when using functional data methods for prediction or hypothesis testing. However, in the present paper we show that this approach is not effective in classification problems. There a useful rule of thumb is that undersmoothing is often desirable, but there are several surprising qualifications to that approach. First, the effect of smoothing the training data can be more significant than that of smoothing the new data set to be classified; second, undersmoothing is not always the right approach, and in fact in some cases using a relatively large bandwidth can be more effective; and third, these perverse results are the consequence of very unusual properties of error rates, expressed as functions of smoothing parameters. For example, the orders of magnitude of optimal smoothing parameter choices depend on the signs and sizes of terms in an expansion of error rate, and those signs and sizes can vary dramatically from one setting to another, even for the same classifier.

Citation

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Raymond J. Carroll. Aurore Delaigle. Peter Hall. "Unexpected properties of bandwidth choice when smoothing discrete data for constructing a functional data classifier." Ann. Statist. 41 (6) 2739 - 2767, December 2013. https://doi.org/10.1214/13-AOS1158

Information

Published: December 2013
First available in Project Euclid: 17 December 2013

zbMATH: 1292.62059
MathSciNet: MR3161446
Digital Object Identifier: 10.1214/13-AOS1158

Subjects:
Primary: 62G08

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.41 • No. 6 • December 2013
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