Pattern recognition procedures derived from a nonparametric estimate of multivariate probability density functions using the orthogonal Hermite system are examined. For sufficiently regular densities, the convergence rate of the mean integrated square error (MISE) isO(n^{-l+\epsilon}),\epsilon >0, wherenis the number of observations and is independent of the dimension. As a consequence, the rate at which the probability of misclassification converges to the Bayes probability of error as the lengthnof the learning sequence tends to infinity is also independent of the dimension of the class densities and equalsO(n^{-1/2+ \delta}), \delta >O.