ASYMPTOTIC BEHAVIOUR OF THE PROBABILITIES OF THE ERRORS

  IN THE CLASSIFICATION PROBLEM WITH GROWING DIMENSION


      Tatjana Pavlenko, Matematisk Statistik i Lund

Discriminant analysis when the number of unknown parameters is
proportional to the number of observations is presented. It is
supposed that the variables are partitioned into an increasing
number of blocks (non-empty subsets) with fixed dimension. In
such a case asymptotic normality of the plug-in discriminant
function has been proved. Based on this result asymptotic
probabilities of misclassification are obtained via the
Kullback-Leibler distance between populations and the relation
between the dimension of the observed vector and the size of
the training samples.