  The ROC curve is the major tool for assessing not only the performance but
also the fairness properties of a similarity scoring function. In order to draw
reliable conclusions based on empirical ROC analysis, accurately evaluating the
uncertainty level related to statistical versions of the ROC curves of interest
is absolutely necessary, especially for applications with considerable societal
impact such as Face Recognition. In this article, we prove asymptotic
guarantees for empirical ROC curves of similarity functions as well as for
by-product metrics useful to assess fairness. We also explain that, because the
false acceptance/rejection rates are of the form of U-statistics in the case of
similarity scoring, the naive bootstrap approach may jeopardize the assessment
procedure. A dedicated recentering technique must be used instead. Beyond the
theoretical analysis carried out, various experiments using real face image
datasets provide strong empirical evidence of the practical relevance of the
methods promoted here, when applied to several ROC-based measures such as
popular fairness metrics.
