Permutation testing in linear models, where the number of nuisance coefficients is smaller than the sample size, is a well-studied topic. The common approach of such tests is to permute residuals after regressing on the nuisance covariates. Permutation-based tests are valuable in particular because they can be highly robust to violations of the standard linear model, such as non-normality and heteroscedasticity. Moreover, in some cases they can be combined with existing, powerful permutation-based multiple testing methods. Here, we propose permutation tests for models where the number of nuisance coefficients exceeds the sample size. The performance of the novel tests is investigated with simulations. In a wide range of simulation scenarios our proposed permutation methods provided appropriate type I error rate control, unlike some competing tests, while having good power.

中文翻译：

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高维线性模型中的置换检验：实证研究

线性模型中的置换测试，其中滋扰系数的数量小于样本量，是一个经过充分研究的主题。此类检验的常用方法是在对干扰协变量进行回归后置换残差。基于排列的测试尤其有价值，因为它们对于违反标准线性模型（例如非正态性和异方差性）具有高度鲁棒性。此外，在某些情况下，它们可以与现有的、强大的基于排列的多重测试方法相结合。在这里，我们建议对滋扰系数数量超过样本量的模型进行置换检验。通过模拟研究了新测试的性能。在广泛的模拟场景中，我们提出的置换方法提供了适当的 I 类错误率控制，与一些竞争测试不同，