Nonparametric statistical inference for P(X

Abstract

Let X, Y and Z be three independent random variables from three different populations. The stress-strength model P(X < Y < Z), the volume under the three-class ROC surface, has extensive applications in various areas since it provides a global measure of differences between or among populations. In this paper, we suggest to make statistical inference for P(X < Y < Z) via two methods, the nonparametric normal approximation and the jackknife empirical likelihood, since the usual empirical likelihood method for U-statistics is too complicated to apply. The results of the simulation studies indicate that these two methods work promisingly compared to other existing methods. Some classical and real data sets were analyzed using these two proposed methods. Practically, for simplicity, the nonparametric normal approximation method should be preferred; for better statistical results, one is suggested to use the JEL method although it is more complex than the normal approximation one. © 2013, Indian Statistical Institute.