Deniz Dutz, Xinyi Zhang
arXiv 8 Dec 2025 · Econometrics
arXiv:2512.07099 · PDF · Extracted main text
Randomization tests yield exact finite-sample Type 1 error control when the null satisfies the randomization hypothesis. However, achieving these guarantees in practice often requires stronger conditions than the null hypothesis of primary interest. For instance, sign-change tests for mean zero require symmetry and fail to control finite-sample error for non-symmetric mean-zero distributions. We investigate whether such limitations stem from specific test choices or reflect a fundamental inability to construct valid randomization tests for certain hypotheses. We develop a framework providing a simple necessary and sufficient condition for when null hypotheses admit randomization tests. Applying this framework to one-sample tests, we provide characterizations of which nulls satisfy this condition for both finite and continuous supports. In doing so, we prove that certain null hypotheses -- including mean zero -- do not admit randomization tests. We further show that nulls that admit randomization tests based on linear group actions correspond only to subsets of symmetric or normal distributions. Overall, our findings affirm that practitioners are not inadvertently incurring additional Type 1 error when using existing tests and further motivate focusing on the asymptotic validity of randomization tests.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Bahadur, Raghu R and Savage, Leonard J (1956) The nonexistence of certain statistical procedures in nonparametric problems | 0.644 | 2 | 2 | 100% |
| 2 | Lehmann, Erich Leo and Romano, Joseph P and Casella, George (1986) Testing statistical hypotheses | 0.511 | 2 | 1 | 100% |
| 3 | Bai, Yuehao and Liu, Jizhou and Shaikh, Azeem M and Tabord-Meehan, Max (2024) Inference in cluster randomized trials with matched pairs | 0.405 | 1 | 1 | 100% |
| 4 | Canay, Ivan A and Romano, Joseph P and Shaikh, Azeem M (2017) Randomization tests under an approximate symmetry assumption | 0.405 | 1 | 1 | 100% |
| 5 | DiCiccio, Cyrus J and Romano, Joseph P (2017) Robust permutation tests for correlation and regression coefficients | 0.405 | 1 | 1 | 100% |
| 6 | Lehmann, EL and Loh, Wei-Yin (1990) Pointwise versus Uniform Robustness of Some Large-Sample Tests and Confidence Intervals | 0.405 | 1 | 1 | 100% |
| 7 | Lei, Lihua and Bickel, Peter J (2021) An assumption-free exact test for fixed-design linear models with exchangeable errors | 0.405 | 1 | 1 | 100% |
| 8 | Pouliot, Guillaum A (2024) An Exact t-Test | 0.405 | 1 | 1 | 100% |
| 9 | Ritzwoller, David M and Romano, Joseph P and Shaikh, Azeem M (2024) Randomization Inference: Theory and Applications | 0.405 | 1 | 1 | 100% |
| 10 | Romano, Joseph P (1989) Bootstrap and randomization tests of some nonparametric hypotheses | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 14 scored citations.