David M. Ritzwoller, Joseph P. Romano, Azeem M. Shaikh
arXiv 13 Jun 2024 · Econometrics
arXiv:2406.09521 · PDF · DOI · OpenAlex · Extracted main text
We review approaches to statistical inference based on randomization. Permutation tests are treated as an important special case. Under a certain group invariance property, referred to as the “randomization hypothesis,” randomization tests achieve exact control of the Type I error rate in finite samples. Although this unequivocal precision is very appealing, the range of problems that satisfy the randomization hypothesis is somewhat limited. We show that randomization tests are often asymptotically, or approximately, valid and efficient in settings that deviate from the conditions required for finite-sample error control. When randomization tests fail to offer even asymptotic Type 1 error control, their asymptotic validity may be restored by constructing an asymptotically pivotal test statistic. Randomization tests can then provide exact error control for tests of highly structured hypotheses with good performance in a wider class of problems. We give a detailed overview of several prominent applications of randomization tests, including two-sample permutation tests, regression, and conformal inference.
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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 | Lehmann, E. L. and Romano, J. P (2022) Testing Statistical Hypotheses self | 1.000 | 8 | 5 | 100% |
| 2 | Berrett, T. B., Wang, Y., Barber, R. F. and Samworth, R. J (2020) The conditional permutation test for independence while controlling for confounders | 0.843 | 3 | 3 | 100% |
| 3 | Hoeffding, W (1952) The large-sample power of tests based on permutations of observations | 0.843 | 3 | 3 | 100% |
| 4 | Kim, I., Balakrishnan, S. and Wasserman, L (2022) Minimax optimality of permutation tests | 0.737 | 3 | 2 | 100% |
| 5 | Bai, Y., Romano, J. P. and Shaikh, A. M (2022) Inference in experiments with matched pairs self | 0.693 | 9 | 1 | 100% |
| 6 | Canay, I. A., Romano, J. P. and Shaikh, A. M (2017) Randomization tests under an approximate symmetry assumption self | 0.693 | 6 | 1 | 100% |
| 7 | Chung, E. and Romano, J. P (2016) Asymptotically valid and exact permutation tests based on two-sample $U$-statistics self | 0.644 | 2 | 2 | 100% |
| 8 | Lehmann, E. L (1949) Some comments on large sample tests | 0.644 | 2 | 2 | 100% |
| 9 | Chung, E. and Romano, J. P (2013) Exact and asymptotically robust permutation tests self | 0.585 | 3 | 1 | 100% |
| 10 | Miller, J. B. and Sanjurjo, A (2018) Surprised by the hot hand fallacy? a truth in the law of small numbers | 0.585 | 3 | 1 | 100% |
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