"A Variable Selection Criterion for Linear Discriminant Rule and its Optimality in High Dimensional Setting"

In this paper, we suggest the new variable selection procedure, called MEC, for linear discriminant rule in the high-dimensional setup. MEC is derived as a second-order unbiased estimator of the misclassication error probability of the lin- ear discriminant rule. It is shown that MEC not only decomposes into `tting' and `penalty' terms like AIC and Mallows C_p, but also possesses an asymptotic optimal- ity in the sense that MEC achieves the smallest possible conditional probability of misclassication in candidate variable sets. Through simulation studies, it is shown that MEC has good performances in the sense of selecting the true variable sets.