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We study a nonparametric test procedure based on order statistics for testing the null hypothesis of equality of two continuous distributions. The exact null distribution of the proposed test statistic is obtained using an enumeration method and a novel combinatorial argument. A recurrence relation for the probability generating function and a sequential approach for computing the mean and variance of the distribution are given. Critical values and characteristics of the distribution for selected small sample sizes are presented. For the Lehmann alternative family, the exact power function of the new test is derived, and its power performance is examined. We also study the power performance of the proposed test under the location-shift and scale-shift alternatives using Monte Carlo simulations and observe its superior performance when compared to commonly used nonparametric tests under various scenarios. A generalization of the proposed procedure for unequal sample sizes is discussed. An illustrative example and some concluding remarks are provided. [ABSTRACT FROM AUTHOR]

In this note we propose a new semi-parametric bootstrap procedure for hypothesis tests about a statistical function and termed bootstrap warping. This procedure was motivated by empirical likelihood and bootstrap tilting techniques. The procedure is computationally efficient and has a fixed number of parameters. We show that the warping procedure has good type I error control and has monotone power as a function of sample size and shift alternatives. [ABSTRACT FROM AUTHOR]