Quasi-randomization-based inference for multivariate Mann-Whitney effects under random missingness
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 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.
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BibTeX
@misc{dobler2026quasirandomizationbased,
title = {{Quasi-randomization-based inference for multivariate Mann-Whitney effects under random missingness}},
author = {Dennis Dobler and Jörg-Tobias Kuhn and Lubna Amro and Paavo Sattler},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07435},
eprint = {2609.07435},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07435},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quasi-randomization-based inference for multivariate Mann-Whitney effects under random missingness
AU - Dennis Dobler
AU - Jörg-Tobias Kuhn
AU - Lubna Amro
AU - Paavo Sattler
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.07435
UR - https://arxiv.org/abs/2609.07435
AB - 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.
ER -