🤖 AI Summary
本文针对随机缺失数据下的重复测量和因子设计，提出了广义多元Mann-Whitney-U检验方法，并通过随机置换改进了I型错误控制。
📝 Abstract
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 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.