Liu Guanfu, Fu Yuejiao, Zhang Jianjun, Pu Xiaolong, Wang Boying
School of Statistics and Information, Shanghai University of International Business and Economics, Shanghai, People's Republic of China.
Department of Mathematics and Statistics, York University, Toronto, Canada.
J Appl Stat. 2019 Aug 8;47(4):724-738. doi: 10.1080/02664763.2019.1652254. eCollection 2020.
In many applications such as case-control studies with contaminated controls, or the test of a treatment effect in the presence of nonresponders in biological experiments or clinical trials, a two-sample problem with one of the samples having a mixture structure often arises. Due to the importance and wide applications of scale mixtures and location mixtures, we consider in this paper the case that the component densities differ only in scale parameters and the case that the component densities differ only in location parameters, and further construct an EM-test for the two-sample problem under each case. We show that both the EM-tests possess a chi-squared null limiting distribution. The local power analysis and sample size calculations are also investigated. Finally, the simulation studies and real data analysis demonstrate that the proposed EM-tests have better performance than the existing methods.
在许多应用中，如使用受污染对照的病例对照研究，或在生物实验或临床试验中存在无反应者的情况下对治疗效果的检验，经常会出现一个两样本问题，其中一个样本具有混合结构。由于尺度混合和位置混合的重要性和广泛应用，我们在本文中考虑成分密度仅在尺度参数上不同的情况以及成分密度仅在位置参数上不同的情况，并进一步针对每种情况构建用于两样本问题的EM检验。我们表明这两种EM检验都具有卡方零极限分布。还研究了局部功效分析和样本量计算。最后，模拟研究和实际数据分析表明，所提出的EM检验比现有方法具有更好的性能。
