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Discriminant analysis using empirical distribution function
Journal of the Korean Data & Information Science Society 2017;28:1179-89
Published online September 30, 2017
© 2017 Korean Data & Information Science Society.

Jae Young Kim1 · Chong Sun Hong2

1Research Institute of Applied Statistics, Sungkyunkwan University
2Department of Statistics, Sungkyunkwan University
Correspondence to: Chong Sun Hong
Professor, Department of Statistics, Sungkyunkwan University, Seoul 03063 Korea. E-mail:
Received July 18, 2017; Revised September 5, 2017; Accepted September 7, 2017.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
In this study, we propose an alternative method for discriminant analysis using a multivariate empirical distribution function to express multivariate data as a simple one-dimensional statistic. This method turns to be the estimation process of the optimal threshold based on classification accuracy measures and an empirical distribution function of data composed of classes. This can also be visually represented on a two-dimensional plane and discussed with some measures in ROC curves, surfaces, and manifolds. In order to explore the usefulness of this method for discriminant analysis in the study, we conducted comparisons between the proposed method and the existing methods through simulations and illustrative examples. It is found that the proposed method may have better performances for some cases.
Keywords : Accuracy, AUC, classification, HUM, threshold, VUS