The discrimination power of projection pursuit with different density estimators

<?Pub Caret> 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. Copyright Biometrika Trust 2002, Oxford University Press.