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.
mX i=1 ∥vi∥2 2 ≥ mX i=1 ti + 1 2 cS # ≤e (− 1 2 c+a2λ)λS By settingλ= min( c 4a2 , ln1.25 n S ), we obtain P
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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.