Interval estimation in discriminant analysis for large dimension

Abstract

ABSTRACTThis paper is concerned with the interval estimation for the log odds of the posterior probability that the observation vector belongs to one of two homoscedastic multivariate normal distributions (Π1 and Π2). We give the limiting distribution of the unbiased estimator for the log odds as the sample sizes and the dimension jointly tend to infinity, and approximate the confidence interval based on the asymptotic distribution. Small-scale simulations are performed to check the precision of the approximation.