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.
Sample complexity bounds for robust mean estimation with mean-shift contamination
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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.