Almost sure convergence of classification procedures using Hermite series density estimates

Authors:
Wodzimierz Greblicki;Mirosaw Pawlak
Affiliations:
Institute of Engineering Cybernetics, Technical University of Wrocaw, 50-370 Wrocaw, Poland;Institute of Engineering Cybernetics, Technical University of Wrocaw, 50-370 Wrocaw, Poland
Venue:
Pattern Recognition Letters
Year:
1983

Citing 2
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Asymptotic efficiency of classifying procedures using the Hermite series estimate of multivariate probability densities (Corresp.)

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Abstract

A multidimensional classification procedure is examined derived from the multiple Hermite series estimate of probability density functions. Conditions for the almost sure convergence of the integrated square error for the estimate are presented and the rate of the convergence is studied. The probability of misclassification, conditioned on a learning sequence of length n, is shown to converge to the Bayes risk almost surely as rapidly as O(n^-^1^2^+^@d), @d positive.