More efficient exact group invariance testing: using a representative subgroup

• 成果类型: Article; Early Access
• 署名作者: Koning, N. W.; Hemerik, J.
• 署名单位: Erasmus University Rotterdam; Erasmus University Rotterdam - Excl Erasmus MC; Wageningen University & Research
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asad050
• 发表日期: 2023
• 关键词: permutation inference; randomization tests; multiple; confidence

摘要

We consider testing invariance of a distribution under an algebraic group of transformations, such as permutations or sign flips. As such groups are typically huge, tests based on the full group are often computationally infeasible. Hence, it is standard practice to use a random subset of transformations. We improve upon this by replacing the random subset with a strategically chosen, fixed subgroup of transformations. In a generalized location model, we show that the resulting tests are often consistent for lower signal-to-noise ratios. Moreover, we establish an analogy between the power improvement and switching from a t-test to a Z-test under normality. Importantly, in permutation-based multiple testing, the efficiency gain with our approach can be huge, since we attain the same power with many fewer permutations.