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Biometrika 2002 89(1):129-143; doi:10.1093/biomet/89.1.129
© 2002 by Biometrika Trust
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The discrimination power of projection pursuit with different density estimators

Olivier Renaud1

1 Faculty of Psychology and Education, University of Geneva, Bd du Pont d'Arve 40, 1211 Geneva 4, Switzerland olivier.renaud{at}pse.unige.ch

We explore the properties of projection pursuit discriminant analysis.This discriminant method is very powerful but relies heavily on a univariate density estimate. We show that the procedure based on wavelets maintains the same rate of convergence as with univariate wavelet density estimation. We also show the Bayes risk strong consistency of both the kernel- and wavelet-based methods. Simulated data and real data concerning character recognition show that the method is effective and robust against the curse of dimensionality. The wavelet alternative seems more likely than the kernel counterpart to find an interesting projection. Wavelets are often criticised for giving too wiggly an estimate and for being too localised to give good global properties. In the above context, these potential drawbacks do not weaken the method but the use of wavelets seems to enhance it. A multiple projection generalisation is also considered.

Key Words: Bayes risk; Discriminant analysis; Kernel; Minimax; Strong consistency; Wavelet

Received June 2000. Revised March 2001


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