In many applied sciences a popular analysis strategy for high-dimensional data is to fit many multivariate generalized linear models in parallel. This paper presents a novel approach to address the resulting multiple testing problem by combining a recently developed sign-flip test with permutation-based multiple-testing procedures. Our method builds upon the univariate standardized flip-scores test which offers robustness against misspecified variances in generalized linear models, a crucial feature in high-dimensional settings where comprehensive model validation is particularly challenging. We extend this approach to the multivariate setting, enabling adaptation to unknown response correlation structures. This approach yields relevant power improvements over conventional multiple testing methods when correlation is present.

翻译：在许多应用科学领域，对高维数据进行分析的一种流行策略是并行拟合多个多元广义线性模型。本文提出了一种新颖的方法，通过将最近开发的符号翻转检验与基于置换的多重检验程序相结合，来解决由此产生的多重检验问题。我们的方法建立在单变量标准化翻转分数检验的基础上，该检验能够有效应对广义线性模型中方差设定错误的情况——这一特性在高维场景中尤为重要，因为在此类场景下进行全面模型验证尤为困难。我们将此方法扩展到多元设置，使其能够适应未知的响应相关结构。当响应变量之间存在相关性时，相较于传统的多重检验方法，本方法能显著提升检验功效。