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Asymptotic properties of the misclassification rates for Euclidean Distance Discriminant rule in high-dimensional data

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  • Watanabe, Hiroki
  • Hyodo, Masashi
  • Seo, Takashi
  • Pavlenko, Tatjana

Abstract

Performance accuracy of the Euclidean Distance Discriminant rule (EDDR) is studied in the high-dimensional asymptotic framework which allows the dimensionality to exceed sample size. Under mild assumptions on the traces of the covariance matrix, our new results provide the asymptotic distribution of the conditional misclassification rate and the explicit expression for the consistent and asymptotically unbiased estimator of the expected misclassification rate. To get these properties, new results on the asymptotic normality of the quadratic forms and traces of the higher power of Wishart matrix, are established. Using our asymptotic results, we further develop two generic methods of determining a cut-off point for EDDR to adjust the misclassification rates. Finally, we numerically justify the high accuracy of our asymptotic findings along with the cut-off determination methods in finite sample applications, inclusive of the large sample and high-dimensional scenarios.

Suggested Citation

  • Watanabe, Hiroki & Hyodo, Masashi & Seo, Takashi & Pavlenko, Tatjana, 2015. "Asymptotic properties of the misclassification rates for Euclidean Distance Discriminant rule in high-dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 234-244.
    • Handle: RePEc:eee:jmvana:v:140:y:2015:i:c:p:234-244
    DOI: 10.1016/j.jmva.2015.05.008
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    References listed on IDEAS

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    1. Makoto Aoshima & Kazuyoshi Yata, 2014. "A distance-based, misclassification rate adjusted classifier for multiclass, high-dimensional data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(5), pages 983-1010, October.
    2. Srivastava, Muni S., 2006. "Minimum distance classification rules for high dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 97(9), pages 2057-2070, October.
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    Cited by:

    1. Makoto Aoshima & Kazuyoshi Yata, 2019. "Distance-based classifier by data transformation for high-dimension, strongly spiked eigenvalue models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(3), pages 473-503, June.
    2. Ishii, Aki & Yata, Kazuyoshi & Aoshima, Makoto, 2022. "Geometric classifiers for high-dimensional noisy data," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    3. 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).

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