CIRJE-F-872 "A Variable Selection Criterion for Linear Discriminant Rule and its Optimality in High Dimensional Setting"
Author Name

Hyodo, Masashi and Tatsuya Kubokawa

Date December 2012
Full Paper   PDF file
Remarks   Revised in February 2013; the title is changed as “A variable selection criterion for linear discriminant rule and its optimality in high dimensional and large sample setting”,subsequently published in Journal of Multivariate Analysis, 123, 364-379 (2014).
Abstract
  

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 misclassi cation 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 Cp, but also possesses an asymptotic optimal- ity in the sense that MEC achieves the smallest possible conditional probability of misclassi cation in candidate variable sets. Through simulation studies, it is shown that MEC has good performances in the sense of selecting the true variable sets.