A variable selection criterion for linear discriminant rule and its optimality in high dimensional and large sample data

In this paper, we suggest the new variable selection procedure, called MEC, for linear discriminant rule in the high dimensional and large sample setup. MEC is derived as a second-order unbiased estimator of the misclassification error probability of the linear discriminant rule (LDR). It is shown that MEC not only asymptotically decomposes into ‘fitting’ and ‘penalty’ terms like AIC and Mallows CpCp, but also possesses an asymptotic optimality in the sense that MEC achieves the smallest possible conditional probability of misclassification in candidate variable sets. Through simulation studies, it is shown that MEC has good performances in the sense of selecting the true variable sets.