In many life science experiments or medical studies, subjects are repeatedly observed and measurements are collected in factorial designs with multivariate data. The analysis of such multivariate data is typically based on multivariate analysis of variance (MANOVA) or mixed models, requiring complete data, and certain assumption on the underlying parametric distribution such as continuity or a specific covariance structure, e.g., compound symmetry. However, these methods are usually not applicable when discrete data or even ordered categorical data are present. In such cases, nonparametric rank-based methods that do not require stringent distributional assumptions are the preferred choice. However, in the multivariate case, most rank-based approaches have only been developed for complete observations. It is the aim of this work is to develop asymptotic correct procedures that are capable of handling missing values, allowing for singular covariance matrices and are applicable for ordinal or ordered categorical data. This is achieved by applying a wild bootstrap procedure in combination with quadratic form-type test statistics. Beyond proving their asymptotic correctness, extensive simulation studies validate their applicability for small samples. Finally, two real data examples are analyzed.
翻译:在许多生命科学实验或医学研究中,反复观察科目,用多变量数据进行保理设计,收集测量数据;分析这种多变量数据通常基于对差异(MANOVA)或混合模型的多变量分析,需要完整的数据,以及对连续性或特定共变结构等基本参数分布的某些假设,例如复度对称;然而,当存在离散数据或甚至定购绝对数据时,这些方法通常不适用;在这种情况下,不要求严格分配假设的非参数级数方法是首选方法;然而,在多变量情况下,大多数基于级数的方法仅用于完整的观测,目的是开发出能够处理缺失值的无参数正确程序,允许单一的常变矩阵,并适用于正态或定购的绝对数据;在使用野生靴带程序与二次形式类型的测试统计数据相结合,从而实现这一点。除了证明它们具有防腐蚀性正确性外,大量模拟研究还验证其对小样品的适用性,最后,两个真实数据是分析。