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Radial confidence regions for ROC surface
Journal of the Korean Data & Information Science Society 2018;29:1109-18
Published online September 30, 2018
© 2018 Korean Data and Information Science Society.

Chong Sun Hong1 · Sang Su Kim2

12Department of Statistics, Sungkyunkwan University
Correspondence to: Professor, Department of Statistics, Sungkyunkwan University, 25-2, Seonggyungwan-ro, Jongno-gu, Seoul, Korea. E-mail:
Received August 16, 2018; Revised September 13, 2018; Accepted September 17, 2018.
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.
There exist the vertical, threshold, and radial confidence bands for the ROC curve. For the radial confidence bands, two kind measures of the confidence interval length in the polar coordinate are proposed by using all confidence intervals of FPR (false positive rate) and TPR (true positive rate). These measures maintain the advantages of the vertical and threshold confidence bands, and complement their disadvantages. Moreover, this method is easily expressed visually. And the ROC surface is extended to propose a radial confidence region. The radial confidence region can utilize all three types of confidence intervals of the probabilities of correct classification, which are components of the ROC surface. There is an advantage that the confidence region can be expressed by focusing on a specific threshold. Also, one can find some superiority of the radial confidence region by comparing with threshold confidence region.
Keywords : Confidence band, confidence region, polar coordinate, radial, threshold.