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Error Bounds for Asymptotic Approximations of the Linear Discriminant Function When the Sample Sizes and Dimensionality are Large

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  • Fujikoshi, Yasunori

Abstract

Theoretical accuracies are studied for asymtotic approximations of the expected probabilities of misclassification (EPMC) when the linear discriminant function is used to classify an observation as coming from one of two multivariate normal populations with a common covariance matrix. The asymptotic approximations considered are the ones under the situation where both the sample sizes and the demensionality are large. We give explicit error bounds for asymptotic approximations of EPMC, based on a general approximation result. We also discuss with a method of obtaining asymptotic expansions for EPMC and their error bounds.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:73:y:2000:i:1:p:1-17
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    References listed on IDEAS

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    1. Saranadasa, H., 1993. "Asymptotic Expansion of the Misclassification Probabilities of D- and A-Criteria for Discrimination from Two High Dimensional Populations Using the Theory of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 46(1), pages 154-174, July.
    2. Ryoichi Shimizu & Yasunori Fujikoshi, 1997. "Sharp Error Bounds for Asymptotic Expansions of the Distribution Functions for Scale Mixtures," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(2), pages 285-297, June.
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    Cited by:

    1. 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.
    2. Raudys, Sarunas & Young, Dean M., 2004. "Results in statistical discriminant analysis: a review of the former Soviet Union literature," Journal of Multivariate Analysis, Elsevier, vol. 89(1), pages 1-35, April.
    3. Shutoh, Nobumichi & Hyodo, Masashi & Seo, Takashi, 2011. "An asymptotic approximation for EPMC in linear discriminant analysis based on two-step monotone missing samples," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 252-263, February.
    4. 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.
    5. Akita, Tomoyuki & Jin, Jinghua & Wakaki, Hirofumi, 2010. "High-dimensional Edgeworth expansion of a test statistic on independence and its error bound," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1806-1813, September.
    6. Tatsuya Kubokawa & Masashi Hyodo & Muni S. Srivastava, 2011. "Asymptotic Expansion and Estimation of EPMC for Linear Classification Rules in High Dimension," CIRJE F-Series CIRJE-F-818, CIRJE, Faculty of Economics, University of Tokyo.

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