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.
LetK ′ ={k|tr(P πk)≤m, 1 2 vT πk v+∥H Zπk v∥2 2 ≤λ 2(X, Z,P K, 1 4 α)} Then|K ′ | ≥(1− 1 4 α)(1 +K)− 1 8 α(1 +K) = (1− 3 8 α)(1 +K)
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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.