We propose two general methods for constructing robust permutation tests under data corruption. The proposed tests effectively control the non-asymptotic type I error under data corruption, and we prove their consistency in power under minimal conditions. This contributes to the practical deployment of hypothesis tests for real-world applications with potential adversarial attacks. One of our methods inherently ensures differential privacy, further broadening its applicability to private data analysis. For the two-sample and independence settings, we show that our kernel robust tests are minimax optimal, in the sense that they are guaranteed to be non-asymptotically powerful against alternatives uniformly separated from the null in the kernel MMD and HSIC metrics at some optimal rate (tight with matching lower bound). Finally, we provide publicly available implementations and empirically illustrate the practicality of our proposed tests.

提出了两种构建在数据损坏下鲁棒的排列检验的方法，能有效控制非渐近型I型错误，并证明在最小条件下的功效一致性，在实际应用中有助于假设检验的部署，特别适用于可能的对抗攻击。其中一种方法具有差分隐私，并进一步扩大了其在私有数据分析中的适用性。对于双样本和独立性设置，我们展示了我们的核鲁棒检验是极小化准则下的最佳，意味着它们在某些最佳速率下（紧密匹配下界）能保证非渐近地对抗空值在核MMD和HSIC度量下的备择假设有力。最后，我们提供了可公开访问的实现，并实证了我们提出测试的实用性。

数据损坏下的鲁棒核假设检验