Asymptotic approximation of EPMC for linear discriminant analysis using ridge type estimator in high-dimensional data with fewer observations

In this paper, the problem of classifying a new observation vector into one of the two normal populations for high-dimensional data is considered.High-dimensional data means that the total number of observation vectors from the two groups is less than the dimension of the observation vectors.Recently, linear discriminant analysis (LDA) for high-dimensional data such as microarray data has been considered.A simple way is to use the Moore-Penrose inverse when the sample covariance matrix is singular.In this paper, we suggest another type LDA approach for high-dimensional data.This method is based on a ridge type estimator of covariance matrix which was proposed by Srivastava and Kubokawa (2008).In addition, we derive asymptotic approximation of EPMC for this method in the situation of n = O(p ), p , 0 < < 1/2.