On constructing accurate confidence bands for ROC curves through smooth resampling

Patrice Bertail (1, 2) , Stéphan Clémençon (3) , Nicolas Vayatis (4)

1 CREST - Centre de Recherche en Économie et Statistique
2 MODAL'X - Modélisation aléatoire de Paris X
3 LTCI - Laboratoire Traitement et Communication de l'Information
4 CMLA - Centre de Mathématiques et de Leurs Applications

This paper is devoted to thoroughly inves- tigating how to bootstrap the ROC curve, a widely used visual tool for evaluating the accuracy of test/scoring statistics s(X) in the bipartite setup. The issue of confidence bands for the ROC curve is considered and a resampling procedure based on a smooth ver- sion of the empirical distribution called the ”smoothed bootstrap” is introduced. Theo- retical arguments and simulation results are presented to show that the ”smoothed boot- strap” is preferable to a ”naive” bootstrap in order to construct accurate confidence bands.

Mots clés: ROC curve; confidence band; functional estimation; bootstrap; smoothing; asymptotic accuracy

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Patrice Bertail, Stéphan Clémençon, Nicolas Vayatis. On constructing accurate confidence bands for ROC curves through smooth resampling. 2008. ⟨hal-00335232⟩