This paper is concerned with selection of variables in two-group discriminant analysis with the same covariance matrix. We propose a test-based method (TM) drawing on the significance of each variable. Sufficient conditions for the test-based method to be consistent are provided when the dimension and the sample size are large. For the case that the dimension is larger than the sample size, a ridge-type method is proposed. Our results and tendencies therein are explored numerically through a Monte Carlo simulation. It is pointed that our selection method can be applied for high-dimensional data.

Principal component analysis is a method for reduction of dimensionality of data in the form of N observations of p variables. In this study we consider estimating the number of the largest characteristic roots of the covariance matrix of p variables, which is called the dimensionality, in a covariance structure such that the remainder characteristic roots are the same. Our purpose is to examine properties of the estimation criteria AIC and BIC based on model selection criteria. Under large-sample asymptotic framework, we evaluate the bias term as an estimator of AIC-type risk. Further, we note that AIC is not consistent, but BIC is consistent. However, for high-dimensional cases, it is pointed out that there are cases that AIC is consistent, but BIC is not consistent, based on a simulation study.