Approximate interval estimation for EPMC for improved linear discriminant rule under high dimensional frame work

Abstract

An observation is to be classified into one of two multivariate normal populations with equal covariance matrix. In this paper, we consider the confidence intervals for expected probability of misclassification (EPMC) for improved linear discriminant rule in two types of data: namely, large sample data and high dimensional data. Our approximate confidence interval is based on the asymptotic normality of consistent estimator of EPMC. Using results of stochastic expression for two bilinear forms and two quadratic forms, we prove asymptotic normality under two different frameworks. Through simulation study, it is observed that our approximate confidence interval has a good performance not only in high dimensional and large sample settings, but also in large sample settings.