Hiroshima Mathematical Journal

EPMC estimation in discriminant analysis when the dimension and sample sizes are large

Tetsuji Tonda, Tomoyuki Nakagawa, and Hirofumi Wakaki

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In this paper we obtain a higher order asymptotic unbiased estimator for the expected probability of misclassification (EPMC) of the linear discriminant function when both the dimension and the sample size are large. Moreover, we evaluate the mean squared error of our estimator. We also present a numerical comparison between the performance of our estimator and that of the other estimators based on Okamoto (1963, 1968) and Fujikoshi and Seo (1998). It is shown that the bias and the mean squared error of our estimator are less than those of the other estimators.

Article information

Hiroshima Math. J., Volume 47, Number 1 (2017), 43-62.

Received: 15 April 2016
Revised: 25 October 2016
First available in Project Euclid: 13 April 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62H30: Classification and discrimination; cluster analysis [See also 68T10, 91C20]
Secondary: 62F12: Asymptotic properties of estimators

Discriminant analysis Classification High dimensional Asymptotic expansion Expected probability of misclassification


Tonda, Tetsuji; Nakagawa, Tomoyuki; Wakaki, Hirofumi. EPMC estimation in discriminant analysis when the dimension and sample sizes are large. Hiroshima Math. J. 47 (2017), no. 1, 43--62. doi:10.32917/hmj/1492048847. https://projecteuclid.org/euclid.hmj/1492048847

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