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

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) is
O(n^{-l+\epsilon})
,
\epsilon >0
, where
n
is 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 length
n
of the learning sequence tends to infinity is also independent of the dimension of the class densities and equals
O(n^{-1/2+ \delta}), \delta >O
.