Ren Pengcheng, Liu Guanfu, Pu Xiaolong
Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE, School of Statistics, East China Normal University, Shanghai, People's Republic of China.
School of Statistics and Information, Shanghai University of International Business and Economics, Shanghai, People's Republic of China.
J Appl Stat. 2021 Dec 24;50(5):1094-1114. doi: 10.1080/02664763.2021.2017414. eCollection 2023.
Recently, the likelihood ratio (LR) test was proposed to test the homogeneity of a three-sample model with a mixture structure. Because of the presence of the mixture structure, the null limiting distribution of the LR test has a complicated supremum form, which leads to challenges in determining -values. In addition, the LR test cannot control type-I errors well under small to moderate sample size. In this paper, we propose seven generalized fiducial methods to test the homogeneity of the three-sample model. Via simulation studies, we find that our methods perform significantly better than the LR test method in controlling the type-I errors under small to moderate sample size, while they have comparable powers in most cases. A halibut data example is used to illustrate the proposed methods.
最近，似然比（LR）检验被提出来用于检验具有混合结构的三样本模型的齐次性。由于混合结构的存在，LR检验的零极限分布具有复杂的上确界形式，这给确定p值带来了挑战。此外，在中小样本量情况下，LR检验不能很好地控制第一类错误。在本文中，我们提出了七种广义 fiducial 方法来检验三样本模型的齐次性。通过模拟研究，我们发现我们的方法在中小样本量情况下控制第一类错误方面比LR检验方法表现得显著更好，而在大多数情况下它们具有相当的检验功效。使用一个大比目鱼数据示例来说明所提出的方法。
