Robust Extensions of Hotelling’s T² and Related Multivariate Tests: A Systematic Review of Simulation Evidence
Abstract
Hotelling’s T² test is a foundational multivariate statistical method widely used for hypothesis testing involving mean vectors. However, its classical formulation relies on strong assumptions, including multivariate normality, low dimensionality relative to sample size, and the absence of outliers. In recent decades, a growing body of literature has proposed robust extensions of Hotelling’s T² test to address violations of these assumptions, particularly in high-dimensional and contaminated data settings. Despite rapid methodological development, simulation-based evidence on the performance of these robust extensions has not yet been systematically synthesized. Guided by the PRISMA framework, this study conducts a systematic literature review of simulation studies published between 1974 and 2025 that examine robust variants of Hotelling’s T² test and related multivariate tests. Searches were conducted in Scopus and Web of Science, resulting in 35 eligible studies for qualitative synthesis. Using thematic analysis, three major themes were identified: robustness in high-dimensional and small-sample regimes; robustness to distributional deviations and outlier contamination; and calibration and computational robustness through resampling and adaptive procedures. The review highlights the consistent performance advantages of robust methods over the classical Hotelling’s T² test under assumption violations, identifies methodological gaps in simulation design, and provides recommendations for future research.
Keywords: Hotelling’s T² test; robust statistics; high-dimensional data; multivariate tests; simulation study; systematic literature review.
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