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July 2019 Estimation of misclassification probability for a distance-based classifier in high-dimensional data
Hiroki Watanabe, Masashi Hyodo, Yuki Yamada, Takashi Seo
Hiroshima Math. J. 49(2): 175-193 (July 2019). DOI: 10.32917/hmj/1564106544

Abstract

We estimate the misclassification probability of a Euclidean distance-based classifier in high-dimensional data. We discuss two types of estimator: a plug-in type estimator based on the normal approximation of misclassification probability (newly proposed), and an estimator based on the well-known leave-one-out cross-validation method. Both estimators perform consistently when the dimension exceeds the total sample size, and the underlying distribution need not be multivariate normality. We also numerically determine the mean squared errors (MSEs) of these estimators in finite sample applications of high-dimensional scenarios. The newly proposed plug-in type estimator gives smaller MSEs than the estimator based on leave-one-out cross-validation in simulation.

Citation

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Hiroki Watanabe. Masashi Hyodo. Yuki Yamada. Takashi Seo. "Estimation of misclassification probability for a distance-based classifier in high-dimensional data." Hiroshima Math. J. 49 (2) 175 - 193, July 2019. https://doi.org/10.32917/hmj/1564106544

Information

Received: 24 August 2016; Revised: 23 January 2019; Published: July 2019
First available in Project Euclid: 26 July 2019

zbMATH: 07120739
MathSciNet: MR3984991
Digital Object Identifier: 10.32917/hmj/1564106544

Subjects:
Primary: 62H12, 62H30
Secondary: 62E20

Rights: Copyright © 2019 Hiroshima University, Mathematics Program

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Vol.49 • No. 2 • July 2019
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