This article deals with testing simultaneous hypotheses about the mean structure and the covariance structure in models with blocked compound symmetric (BCS) covariance structure. Considered models are used for double multivariate data, which means that m-variate vector of observation is measured repeatedly over u levels of some factor on each of n individual. Additionally, the assumption of multivariate normality for this type of data is made. We use framework of ratio of positive and negative parts of best unbiased estimators to obtain simultaneous F test. The test statistic is constructed as a ratio of test statistics for testing single hypotheses about the mean vector and the covariance matrix. In simulation study power of obtained test is compared with powers of three other F tests—two for testing single hypotheses and one for testing simultaneous hypotheses, whose test statistic is convex combination of test statistics of these two single F tests. The problem of simultaneous testing of the mean vector and covariance matrix was also consider in paper (Hyodo and Nishiyama, Commun Stat Theory Methods, https://doi.org/10.1080/03610926.2019.1639751, 2019).

本文涉及在具有分块复合对称 (BCS) 协方差结构的模型中测试关于平均结构和协方差结构的同时假设。考虑的模型用于双重多元数据，这意味着在n 中的每一个上的某个因子的u 个水平上重复测量m变量观察向量个人。此外，对此类数据进行了多元正态性假设。我们使用最佳无偏估计量的正负部分比率框架来获得同步 F 检验。检验统计量被构造为检验统计量的比率，用于检验关于均值向量和协方差矩阵的单个假设。在模拟研究中，将获得的检验的检验功效与其他三个 F 检验的功效进行比较——两个用于检验单个假设，一个用于检验同时假设，其检验统计量是这两个单一 F 检验的检验统计量的凸组合。论文中还考虑了同时测试均值向量和协方差矩阵的问题（Hyodo 和 Nishiyama，Commun Stat Theory Methods，https://doi.org/10.1080/03610926.2019.1639751，2019）。