带重复测量且观测不完全的非参数因子设计：一种野自助法途径
Incompletely observed nonparametric factorial designs with repeated measurements: A wild bootstrap approach
AI总结：
针对含缺失值、有序分类数据的多变量重复测量因子设计，提出结合野自助法与二次型检验统计量的非参数方法，证明了其渐近正确性并在小样本及真实数据中验证了适用性。
摘要：
在许多生命科学实验或医学研究中，受试者被反复观察，并在因子设计中收集多变量数据的测量值。此类多变量数据的分析通常基于多变量方差分析（MANOVA）或混合模型，这需要完整的数据，并对潜在的参数分布做出某些假设，如连续性或特定的协方差结构（例如复合对称性）。然而，当存在离散数据甚至有序分类数据时，这些方法通常不适用。在这种情况下，不需要严格分布假设的非参数基于秩的方法是首选。然而，在多变量情况下，大多数基于秩的方法仅为完全观测而开发。本工作的目的是开发渐近正确的程序，能够处理缺失值，允许奇异协方差矩阵，并适用于有序或有序分类数据。这是通过将野自助法程序与二次型检验统计量相结合来实现的。除了证明其渐近正确性外，广泛的模拟研究验证了它们在小样本中的适用性。最后，分析了两个真实数据示例。
英文摘要：
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.
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