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：在生命科学实验或医学研究中，受试者常被重复观测，并在多变量数据的析因设计中收集测量值。此类多变量数据的分析通常依赖于多变量方差分析或混合模型，这些方法要求数据完整，并假定潜在的参数分布满足连续性或特定的协方差结构（如复合对称性）。然而，当数据为离散型或有序分类数据时，这些方法通常难以适用。在此类情况下，无需严格分布假设的非参数秩次方法成为首选。然而，在多变量场景下，大多数基于秩次的方法仅适用于完全观测数据。本研究旨在开发渐近正确的方法，能够处理缺失值、允许奇异协方差矩阵，并适用于有序分类数据。通过结合野自助程序与二次型检验统计量实现这一目标。除证明其渐近正确性外，广泛的模拟研究验证了其在中小样本中的适用性。最后，分析了两组实际数据案例。