Title: On the dimension effect of regularized linear discriminant analysis,
Abstract: This paper studies the dimension effect of the linear discriminant analysis
(LDA) and the regularized linear discriminant analysis (RLDA) classifiers for
large dimensional data where the observation dimension $p$ is of the same order
as the sample size $n$. More specifically, built on properties of the Wishart
distribution and recent results in random matrix theory, we derive explicit
expressions for the asymptotic misclassification errors of LDA and RLDA
respectively, from which we gain insights of how dimension affects the
performance of classification and in what sense. Motivated by these results, we
propose adjusted classifiers by correcting the bias brought by the unequal
sample sizes. The bias-corrected LDA and RLDA classifiers are shown to have
smaller misclassification rates than LDA and RLDA respectively. Several
interesting examples are discussed in detail and the theoretical results on
dimension effect are illustrated via extensive simulation studies.