where F1, F2 are cumulative distributions (discrete or continuous) of the observations and Tis their upper limit. The test is shown to be asymptotically normal and consistent against one-sided alternatives F1(t) < F2(t) (t ~ T) and against two-sided alternatives where either F1(t) < F2(t) or F1(t) > F2(t) (t ~ T). The asymptotic efficiency of the test relative to the efficient parametric test w...

We show the combinatorics behind the Wilcoxon-Mann-Whitney two-sample test. This yields new combinatorial proofs of recurrences for its null distribution given recently by Brus and Chang, as well as new recurrences. It is shown how to convert these recurrences into generating functions. These generating functions are used to obtain closed expressions for the null distribution when one of the sa...

The authors present an improved ranked set two-sample Mann-Whitney-Wilcoxon test for a location shift between samples from two distributions F and G. They define a function that measures the amount of information provided by each observation from the two samples, given the actual joint ranking of all the units in a set. This information function is used as a guide for improving the Pitman effic...

Cross entropy and mean squared error are typical cost functions used to optimize classi er performance. The goal of the optimization is usually to achieve the best correct classi cation rate. However, for many two-class real-world problems, the ROC curve is a more meaningful performance measure. We demonstrate that minimizing cross entropy or mean squared error does not necessarily maximize the...

rH..il:ribllltlton.-tr'ee two-sample test is proposed tha t is an extension of the Wilcoxon test with arbitrary censoring on the right. The test is conditional on the pattern ~ha.t~TV:&l>ll~l..lll. The null hypothesis is H0 : F1(t) = F2(t) (t ~ T) agai nst either H1 : F1(t) < F 2(t) (t ~ T) or H2 : F1(t) < F2(t) or F1(t) > F2 (t) (t ~ T), '~here .l\,F2 are cumulative distributions (discrete or ...