On Linear Discriminant Analysis with Adaptive Ridge Classification Rules

Consider the problem in which we have a sample from each of two multivariate normal populations with equal covariance matrices and we wish to classify a new observation as coming from one of the two populations. It is widely regarded that the most commonly used discriminant procedure for this purpose was introduced by Anderson. During the last 15 years, promising linear adaptive ridge classification rules have been proposed as alternatives where the ridge parameters are chosen by sample reuse methods like cross-validation and bootstrap. This article undertakes a large sample study of the relationship between the optimal ridge parameter and the population parameters. The results suggest a new linear adaptive ridge classification procedure which has a simple closed-form expression for the ridge parameter. A Monte Carlo study is used to compare its error rate with that of the other classification rules previously mentioned.