Nonparametric multi-samples test for simple stochastic ordering against unrestricted alternative

Abstract

Statistical inferences under simple stochastic ordering for two continuous populations has a long and rich history. But further study for multiple populations is still expected. In this article, we consider samples test for simple stochastic ordering against unrestricted alternative. A test statistic is constructed with the empirical distribution functions and the isotonic regression estimates of distribution functions, and the null asymptotic distribution of the proposed test statistic is given. A bootstrap procedure is suggested for the critical values, and some simulation results are presented to illustrate the proposed test method.