单因素方差分析模型中的广义p-值

研究非平衡、异方差情况下的单因素方差分析(ANOVA)模型中等均值假设检验问题.首先用Fiducial方法得到广义枢轴向量,由此直接定义广义p-值,并证明了由此广义p-值所给出的检验在边界上具有频率性质.该方法也可以应用于其他的多参数模型.作为例子,又考虑了具有协变量的ANOVA模型中等均值假设检验问题,给出了其检验问题的广义p-值.最后通过数值模拟,对本文方法与Weerahandi方法做了比较.模拟结果表明,在异方差时本文方法优于Weerahandi方法.

The Generalized p-value of the One-way Layout Analysis of Variance Model

This article studies the unbalanced and heterogeneous variances one-way layout analysis of variance (ANOVA) model by the generalized p-value method.The generalized pivotal model is drawn by Fiducial inference, by which the generalized p-value is defined directly. Then the hypotheses test problem is solved and this test is proved to be valid at the boundary. The method of this article can also be used in other models with several parameters. As an example, the ANOVA model with covariant variables is considered. The generalized p-value of this model is given,and then the critical region is proposed. In simulation studies, the method of this article and Weerahandi's are compared.The results show that the generalized p-value given in this article is reasonable.