Limitations of Randomization Tests in Finite Samples

[2512.07099] Limitations of Randomization Tests in Finite Samples Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Economics > Econometrics arXiv:2512.07099 (econ) [Submitted on 8 Dec 2025 ( v1 ), last revised 15 Aug 2026 (this version, v3)] Title: Limitations of Randomization Tests in Finite Samples Authors: Deniz Dutz , Xinyi Zhang View a PDF of the paper titled Limitations of Randomization Tests in Finite Samples, by Deniz Dutz and 1 other authors View PDF HTML (experimental) Abstract: Randomization tests deliver exact finite-sample Type 1 error control when the null satisfies the randomization hypothesis. In practice, achieving these guarantees often requires stronger conditions than the null hypothesis of primary interest. For example, sign-change tests of mean zero require symmetry and need not control finite-sample size for non-symmetric mean-zero distributions. We investigate whether the mismatch between the null and the invariance conditions required for exactness reflects the use of particular transformations or a more fundamental limitation. We provide a simple necessary and sufficient condition for a null hypothesis to admit a randomization test. Applying this framework to one-sample problems, we characterize the nulls that admit randomization tests on finite supports and derive impossibility results on continuous supports. In particular, we show that several common nulls, including mean zero, do not admit randomization tests. We further show that, among one-sample tests using linear group actions, the admissible nulls are limited to subsets of symmetric or Gaussian distributions. These results confirm that the absence of exact finite-sample validity is inherent for many commonly studied nulls and that practitioners using existing tests are not foregoing feasible exact alternatives. Subjects: Econometrics (econ.EM) Cite as: arXiv:2512.07099 [econ.EM] (or arXiv:2512.07099v3 [econ.EM] for this version) https://doi.org/10.48550/arXiv.2512.07099 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Deniz Dutz [ view email ] [v1] Mon, 8 Dec 2025 02:28:23 UTC (20 KB) [v2] Thu, 2 Apr 2026 13:55:35 UTC (22 KB) [v3] Sat, 15 Aug 2026 03:44:48 UTC (40 KB) Full-text links: Access Paper: View a PDF of the paper titled Limitations of Randomization Tests in Finite Samples, by Deniz Dutz and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: econ.EM < prev | next > new | recent | 2025-12 Change to browse by: econ References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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