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

Abstract

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 .