In Efron's two-groups model, adaptive confidence intervals for the null location have minimax length of order σ(n^{-1/4} + ε^{1/2}/sqrt(log(enε²))) when ε unknown and σ known, degrading to Ω(σ n^{-1/8}) when σ unknown; a Fourier certification algorithm attains the known-σ bound.
Adaptive robust confidence intervals
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Sample complexities for robust binary hypothesis testing under three contamination models are unstable in ε but comparable across models up to constant rescaling of ε, with explicit least-favourable distributions for the subtractive model.
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Adaptive Confidence Intervals in Efron's Gaussian Two-Groups Model
In Efron's two-groups model, adaptive confidence intervals for the null location have minimax length of order σ(n^{-1/4} + ε^{1/2}/sqrt(log(enε²))) when ε unknown and σ known, degrading to Ω(σ n^{-1/8}) when σ unknown; a Fourier certification algorithm attains the known-σ bound.
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On the Sample Complexity of Robust Binary Hypothesis Testing
Sample complexities for robust binary hypothesis testing under three contamination models are unstable in ε but comparable across models up to constant rescaling of ε, with explicit least-favourable distributions for the subtractive model.