Cyclic Permutation Test: A Nonstandard Exact Test For Linear Models

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Proposes the Cyclic Permutation Test (CPT) that gives exact finite-sample Type I control for arbitrary fixed design and arbitrary exchangeable errors whenever 1/α is an integer and n/p ≥ 1/α − 1 (e.g. α = 0.05 requires n/p ≥ 19). Constructs 1/α linear statistics by solving a linear system so their joint law is invariant under a cyclic permutation group, applies a marginal rank test to those statistics, and boosts power by optimizing row ordering with a genetic algorithm (simulations show comparable power and an exact confidence interval by inversion).

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" chapters (11)

1. 0:00Introduction and background
2. 3:09Hypothesis testing context
3. 5:56Literature review findings
4. 9:18Challenges of exact testing
5. 11:02Cyclic permutation test
6. 13:34Constructing the test
7. 19:32Power and efficiency
8. 23:12Algorithmic implementation
9. 27:17Simulation performance
10. 30:42Reflections and future work
11. 34:02Closing discussion and Q&A