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An asymptotic approximation for EPMC in linear discriminant analysis based on two-step monotone missing samples

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  • Shutoh, Nobumichi
  • Hyodo, Masashi
  • Seo, Takashi

Abstract

In this paper, we consider the expected probabilities of misclassification (EPMC) in the linear discriminant function (LDF) based on two-step monotone missing samples and derive an asymptotic approximation for the EPMC with an explicit form for the considered LDF. For this purpose, we also provide some results of the expectations for the inverted Wishart matrices in this paper. Finally, we conduct the Monte Carlo simulation for evaluating our result.

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  • 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.
    • Handle: RePEc:eee:jmvana:v:102:y:2011:i:2:p:252-263
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    References listed on IDEAS

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    1. 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.
    2. Yu, Jianqi & Krishnamoorthy, K. & Pannala, Maruthy K., 2006. "Two-sample inference for normal mean vectors based on monotone missing data," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2162-2176, November.
    3. Haff, L. R., 1979. "An identity for the Wishart distribution with applications," Journal of Multivariate Analysis, Elsevier, vol. 9(4), pages 531-544, December.
    4. Chang, Wan-Ying & Richards, Donald St. P., 2010. "Finite-sample inference with monotone incomplete multivariate normal data, II," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 603-620, March.
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    Cited by:

    1. Tsukada, Shin-ichi, 2014. "Asymptotic expansion for distribution of the trace of a covariance matrix under a two-step monotone incomplete sample," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 206-219.
    2. Tatjana Pavlenko & Anuradha Roy, 2013. "Supervised classifiers of ultra high-dimensional higher-order data with locally doubly exchangeable covariance structure," Working Papers 0185mss, College of Business, University of Texas at San Antonio.

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