Asymptotic validity and finite-sample properties of approximate randomization tests
研究了近似随机化检验在数据噪声下的有效性，给出了非渐近界来量化其与理想检验的差异，并通过线性回归等例子说明小样本行为。
Summary Randomization tests rely on simple data transformations and possess an appealing robustness property. In addition to being finite-sample valid if the data distribution is invariant under the transformation, these tests can be asymptotically valid under a suitable studentization of the test statistic, even if the invariance does not hold. However, practical implementation often encounters noisy data, resulting in approximate randomization tests that may not be as robust. In this paper, one key theoretical contribution is a nonasymptotic bound on the discrepancy between the size of an approximate randomization test and the size of the idealized randomization test using noiseless data. This allows us to derive novel conditions for the validity of approximate randomization tests under data invariances, while being able to use existing results based on studentization if the invariance does not hold. We illustrate our theory through several examples, including significance tests in linear regression. These examples clarify key aspects of how randomization tests behave in small samples and address limitations of prior theoretical results.