标题： 对单因素方差分析中树状有序备择假设的检验 显示英文标题

标题： Testing Against Tree Ordered Alternatives in One-way ANOVA

摘要： 首次考虑了一元异方差ANOVA中针对树状有序备择假设的似然比检验。 使用引导法实现此检验以及两种基于多重比较的检验，并显示出非常良好的大小和功效性能。 在本文中，考虑了在异方差一元ANOVA模型中针对树状有序备择假设检验均值效应的同质性问题。 提出了似然比检验和两种基于多重比较的检验——称为Max-D和Min-D，并使用参数引导方法进行实现。 一项广泛的模拟研究显示，这些检验在各种样本大小和误差方差的选择下有效地控制了第一类错误率。 此外，似然比检验和Max-D检验在所有情况下都实现了非常好的功效。 观察到Min-D检验在某些特定的参数配置下表现优于其他两种检验。 通过实施一些非正态分布，如偏正态、拉普拉斯、指数、混合正态和t分布，研究了这些检验的稳健性。 开发并分享了“Github”上的“R”包，以便用户使用。 所提出的检验在一个接受心理治疗的患者数据集上进行了说明。 显示英文摘要

摘要： The likelihood ratio test against a tree ordered alternative in one-way heteroscedastic ANOVA is considered for the first time. Bootstrap is used to implement this and two multiple comparisons based tests and shown to have very good size and power performance. In this paper, the problem of testing the homogeneity of mean effects against the tree ordered alternative is considered in the heteroscedastic one-way ANOVA model. The likelihood ratio test and two multiple comparison-based tests - named Max-D and Min-D are proposed and implemented using the parametric bootstrap method. An extensive simulation study shows that these tests effectively control type-I error rates for various choices of sample sizes and error variances. Further, the likelihood ratio and Max-D tests achieve very good powers in all cases. The test Min-D is seen to perform better than the other two for some specific configurations of parameters. The robustness of these tests is investigated by implementing some non-normal distributions, viz., skew-normal, Laplace, exponential, mixture-normal, and t distributions. `R' packages are developed and shared on "Github" for the ease of users. The proposed tests are illustrated on a dataset of patients undergoing psychological treatments.