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

Author

Listed:
  • Masashi Hyodo

    (Graduate School of Economics, University of Tokyo)

  • Tatsuya Kubokawa

    (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.

Suggested Citation

  • Masashi Hyodo & Tatsuya Kubokawa, 2012. "A Variable Selection Criterion for Linear Discriminant Rule and its Optimality in High Dimensional Setting," CIRJE F-Series CIRJE-F-872, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2012cf872
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    References listed on IDEAS

    as
    1. J. D. Wilbur & J. K. Ghosh & C. H. Nakatsu & S. M. Brouder & R. W. Doerge, 2002. "Variable Selection in High-Dimensional Multivariate Binary Data with Application to the Analysis of Microbial Community DNA Fingerprints," Biometrics, The International Biometric Society, vol. 58(2), pages 378-386, June.
    2. Kubokawa, Tatsuya & Hyodo, Masashi & Srivastava, Muni S., 2013. "Asymptotic expansion and estimation of EPMC for linear classification rules in high dimension," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 496-515.
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