The minimax rate for estimating calibration error is Theta((L epsilon/m)^{1/3}), creating a verification tax that makes auditing harder as models improve.
Asymptotic equivalence of nonparametric regression and white noise
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The Verification Tax: Fundamental Limits of AI Auditing in the Rare-Error Regime
The minimax rate for estimating calibration error is Theta((L epsilon/m)^{1/3}), creating a verification tax that makes auditing harder as models improve.