简单随机序是在概率分布意义下比较随机变量的大小, 被用于许多领域. 两总体简单随机序的检验问题已经有了很多的 研究成果, 但对多总体情况下简单随机序检验问题的研究却很少. 文章考虑多总体情况下简单随机序的检验问题, 利用分布函数的保序回归估计构造出检验统计量, 给出了检验统计量在原假设下的渐近分布; 同时, 利用Bootstrap方法给出了计算临界值和$p$值的方法, 并通过Monte Carlo 模拟来说明文章所提出方法的可实现性 和优良表现.

Stochastic ordering, by which random variables are compared accord- ing to their probability distributions, has been widely employed in practice. Testing against simple stochastic ordering of two distributions has been studied extensively, but there are few works for the case of k > 2 distributions. In this article, we con- sider this case, and construct a test statistic with the isotonic regression estimators of the distribution functions. The null asymptotic distribution of the test statistic is presented, and a procedure to calculate the critical value or p-value based on boot- strapping is given. Finally, simulation results are preseted to illusrae the proposed test method.