Effect of dimensionality on discrimination

Discrimination problems in a high-dimensional setting is considered. New re sults are concerned with the role of the dimensionality in the performance of the discrimination procedure. Assuming that data consist of a block stru cture two different asymptotic approaches are presented. These approaches a re characterized by different types of relations between the dimensionality and the size of the training samples. Asymptotic expressions for the error probabilities are obtained and a consistent approximation of the discrimin ant function is proposed. Throughout the paper the importance of the dimens ionality in the asymptotic analysis is stressed.