高维数据中对抗鲁棒的多重检验
Adversarially robust multiple testing in high dimensions
浏览论文内容
中文总结 AI 辅助
本文提出基于分位数缩尾技术的高维对抗鲁棒多重检验方法，可在对抗污染下近似控制家族式错误率，支持假设数量随样本量指数增长，其两样本结果的不等式扩展具有独立价值。
中文摘要 AI 辅助
本文提出了用于评估高维均值向量坐标相等性限制的鲁棒多重检验方法，该方法基于分位数缩尾技术，在对抗污染下近似控制（强）家族式错误率，且允许假设数量随样本量呈指数增长，仅需略多于二阶矩。技术上，其一样本结果基于近期高维分位数缩尾均值分布的高斯近似不等式，两样本结果基于本文开发的该类不等式扩展，具有独立研究价值。
英文摘要
Robust multiple testing procedures for assessing equality restrictions on the coordinates of high-dimensional mean vectors are proposed. Our procedures are based on quantile-winsorization techniques, approximately control the familywise error rate (strongly) under adversarial contamination, and allow the number of hypotheses to grow exponentially with sample size, despite requiring only slightly more than two moments. Technically, our one-sample results build on recent Gaussian approximation inequalities for the distribution of high-dimensional quantile-winsorized means, whereas our two-sample results are based on extensions thereof, which we develop here and which could be of some interest in their own right.
