Relationship between KS, AUROC, and Gini Common model validation statistics like the Kolmogorov–Smirnov test (KS), AUROC, and Gini coefficient are all functionally related. However, my question has to do with proving how these are all related. I am curious if anyone can help me prove these relationships. I haven't been able to find anything online, but I am just genuinely interested how the proofs work. For example, I know Gini=2AUROC-1, but my best proof involves pointing at a graph. I am interested in formal proofs. Any help would be greatly appreciated!
The Wikipedia entry for Receiver operating characteristic references this paper for the Gini=2AUROC-1 result: Hand, David J.; and Till, Robert J. (2001); A simple generalization of the area under the ROC curve for multiple class classification problems, Machine Learning, 45, 171–186.  But I'm afraid I don't have easy access to it to see how close it comes to what you want.