多项分布总体的相等对增凸序问题的多样本检验

Multi-Sample Testing for the Equality of Multinomial Populations Against Increasing Convex Ordering Alternative

概率分布间随机序在实践中已经得到了广泛的应用,而且似然比检验是用以检验涉及随机序问题的最普遍的检验方法．但是,关于多个多项式总体间的增凸序约束的统计推断问题并没有得到充分发展．多样本的增凸序对无约束的检验问题已被研究．然而,多总体的相等性对增凸序的假设检验问题似乎更有研究意义．并且分布的相等对随机序的假设检验问题往往是统计学家最为普遍地考虑．对多样本的情况,本文考虑了分布的相等对增凸序的假设检验问题,并且获得似然比检验统计量的零渐近分布,它是一组x^2分布随机变量的加权和,即■~2分布．

Stochastic ordering among probability distributions has been widely applied in practice. Likelihood ratio testing is the most commonly used method to test hypotheses involving stochastic orderings. Unfortunately, statistical inference methods based on likelihood ratio principle on increasing convex ordering for more than two multinomial populations have not been fully developed. The problem of testing the increasing convex ordering against no restriction for multi-sample case has been considered by using likelihood ratio test. However, it may be of more interest to test for the equality against the increasing convex ordering alternative among several populations. Testings for the equality againbt order-restricted alternative are most commonly considered by statisticians. This paper considers the equality against the increasing convex ordering for multi-sample case and obtains the null asymptotic distribution of the likelihood ratio test statistic, which is a mixture of chi-squared distributions, that is chi-bar-squared distribution.