Asymptotic Results for Multiple Discriminant Procedures When the Dimension is Large Compared to the Sample Size
by
Yasunori Fujikoshi
Department of Mathematics, Graduate School of Science, Hiroshima University, Japan

This paper is concerned with discriminant procedures for several p-variate normal populations with the same covariance matrix, in the situation where the dimension p is large compared to the sample size n. First we consider the usual test statistics including the dimensionality test and the discriminant powers in terms of the characteristic roots. Some asymptotic results for these statistics are derived under the assumption that p/n tends to c in (0, 1). It is shown that the new asymptotic results are more accurate than the classical large sample asymptotic ones. Next we derive asymptotic results for some high-dimensional discriminant procedures which are compared with the ones of classical discriminant procedures. The asymptotic results obtained in this paper are based on joint works with H. Wakaki, V. Ulyanov and T. Himeno.

Date received: August 28, 2003