Group permutation tests control Type I error at most 2α (sharp) for linear model coefficients, improve power over i.i.d. permutations via design-adaptive group choice, and extend to non-exchangeable errors with TV-distance degradation bounds.
54 B.2.3 Formal version of Theorem 5 We provide Theorem 16, the formal version of Theorem 5 and complete its proof here
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Group Permutation Testing in Linear Model: Sharp Validity, Power Improvement, and Extension Beyond Exchangeability
Group permutation tests control Type I error at most 2α (sharp) for linear model coefficients, improve power over i.i.d. permutations via design-adaptive group choice, and extend to non-exchangeable errors with TV-distance degradation bounds.