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

Masashi Hyodo and Tatsuya Kubokawa
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Masashi Hyodo: Graduate School of Economics, University of Tokyo
Tatsuya Kubokawa: Faculty of Economics, University of Tokyo

No CIRJE-F-872, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

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 C p , 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.

Pages: 23 pages
Date: 2012-12
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