Pages 115-118
The problem of classifying a new observation vector into one of the two known groups distributed as multivariate normal with common covariance matrix is considered. In this paper, we handle the situation that the dimension, p, of the observation vectors is less than the total number, N, of observation vectors from the two groups, but both p and N tend to infinity with the same order. Since the inverse of the sample covariance matrix is close to an ill condition in this situation, it may be better to replace it with the inverse of the ridge-type estimator of the covariance matrix in the linear discriminant analysis (LDA). The resulting rule is called the ridge-type linear discriminant analysis (RLDA). The second-order expansion of the expected probability of misclassifkation (EPMC) for RLDA is derived by Kubokawa, Hyodo and Srivastava (2011), and the second-order unbiased estimator of EMPC is also given. In this study, the estimation accuracy of the second-order unbiased estimator of EPMC is investigated by using Monte Carlo simulation.
