Rank statistics expressible as integrals under P-P-plots and receiver operating characteristic curves

Given a probability measure on the unit square, the measure of the region u nder an empirical P-P-plot defines a two-sample rank statistic. Instances i nclude trimmed and censored versions of the Mann-Whitney-Wilcoxon statistic and a class of statistics with applications in the analysis of receiver op erating characteristic (ROC) curves. A large sample distribution for such a statistic is obtained, which is valid under sampling from general populati ons. Explicit results are presented for comparing arbitrary quantile segmen ts of two populations. The results are not restricted to continuous data an d incorporate adjustments for tied values in the discrete case. A multivari ate version of the large sample distribution extends the class of tractable statistics in ROC analysis and facilitates the use of methods based on par tial areas when the data are discrete.