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

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  • Hyodo, Masashi
  • Kubokawa, Tatsuya

Abstract

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 Cp, 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.

Suggested Citation

  • Hyodo, Masashi & Kubokawa, Tatsuya, 2014. "A variable selection criterion for linear discriminant rule and its optimality in high dimensional and large sample data," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 364-379.
    • Handle: RePEc:eee:jmvana:v:123:y:2014:i:c:p:364-379
    DOI: 10.1016/j.jmva.2013.10.005
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    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. Fujikoshi, Yasunori, 2000. "Error Bounds for Asymptotic Approximations of the Linear Discriminant Function When the Sample Sizes and Dimensionality are Large," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 1-17, April.
    3. Fujikoshi, Yasunori, 1985. "Selection of variables in two-group discriminant analysis by error rate and Akaike's information criteria," Journal of Multivariate Analysis, Elsevier, vol. 17(1), pages 27-37, August.
    4. 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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    Cited by:

    1. Nakagawa, Tomoyuki & Watanabe, Hiroki & Hyodo, Masashi, 2021. "Kick-one-out-based variable selection method for Euclidean distance-based classifier in high-dimensional settings," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    2. Michael Asamoah-Boaheng & Atinuke Adebanji & Morire Labeodan, 2016. "Some zero mean classification functions with unequal prior probabilities and non-normality," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 5(3), pages 2.

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