Effect of dimensionality on discrimination
Tatjana Pavlenko, Dietrich von Rosen · Statistics · 2001
Discrimination problems in a high-dimensional setting is considered. New results are concerned with the role of the dimensionality in the performance of the discrimination procedure. Assuming that data consist of a block structure two different asymptotic approaches are presented. These approaches are 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 discriminant function is proposed. Throughout the paper the importance of the dimensionality in the asymptotic analysis is stressed.