I am wondering how the confidence interval for the Area under the Curve statistic (ROC curves) is derived. I have heard that the AUC can be assumed to be normally distributed, but I am looking for a proof of this statement or a derivation of the confidence intervals
AUC Distribution – Understanding the Distribution of the AUC in Logistic Classification
aucclassificationlogisticroc
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Best Answer
AUC can be viewed as Wilcoxon-Mann-Whitney Test. And here is some demo, where for the R code I posted, I first calculate AUC, then use Wilcoxon-Mann-Whitney Test to calculate the number. Then verify both numbers are the same which is 0.911332. For a hypothesis testing, it is not hard to derive confidence interval. Right? Also I do not remember it Wilcoxon-Mann-Whitney Test requires normal distribution.