广义多变量Mann-Whitney-$U$检验及随机缺失下相对效应的置信区域
Quasi-randomization-based inference for multivariate Mann-Whitney effects under random missingness
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中文总结 AI 辅助
本文提出广义多变量Mann-Whitney-U检验，处理随机缺失数据下的重复测量与因子设计，结合随机置换实现渐近精确检验并改善第一类错误控制，模拟和实例验证其小样本优势。
中文摘要 AI 辅助
边际Mann-Whitney效应在各研究领域被广泛使用，且该估计量的扩展已在统计方法学的多个方向上得到发展。本文聚焦于针对重复测量和因子设计在随机缺失数据情形下的扩展。在Rubarth等人（2022a）的前期工作中，在确定性缺失指标的假设下开发了渐近正确的检验。相比之下，本文的方法考虑了现实机制下缺失值的随机性质。因此，所涉及的协方差矩阵纳入了缺失数据的真实变异性。结合在每个数据点内使用随机置换的随机化程序，可得到渐近精确的检验，并总体上改善了对第一类错误的控制。此外，在可交换抽样分布的特殊情况下，这些检验在有限样本量下也能控制第一类错误。在广泛设置下的模拟实验证明了所提方法在小样本中的优势，也适用于不同的缺失机制。一项关于学童学习数学的真实数据分析说明了该检验应用的多个实际方面。
英文摘要
Marginal Mann-Whitney effects are widely used across various fields of research, and extensions of this estimand have been developed in many directions in statistical methodology. In this paper, we focus on an extensions for repeated measurements and factorial designs subject to randomly missing data. In a previous work by Rubarth et al. (2022a), asymptotically correct tests were developed under the assumption of deterministic missing indicators. In contrast, the approach in the present paper accounts for the stochastic nature of missing values under realistic mechanisms. Thus, the involved covariance matrix incorporates the true variability of missing data. The combination with a quasi-randomization procedure using random permutations within each data point yields asymptotically exact tests and a generally improved type-I error control. Additionally, the tests control the type-I error for finite sample sizes in the special case of exchangeable sampling distributions. Simulations across a wide range of settings demonstrate the benefits of the proposed method in small samples, also for different missingness mechanisms. A real data analysis about school children learning math illustrates several practical aspects of the tests' application.
发表机构
- RWTH Aachen University（亚琛工业大学）
- TU Dortmund University（多特蒙德工业大学）
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