The paper develops an order-optimal adaptive 1-bit mean estimator for distributions with bounded k-th moments and proves a novel lower bound for the variance case.
1 ĎDpλ, σqconstructed in the proof of Theorem 9, whereN“λ{σ´1. We will again establish a lower bound for this “hard subset
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Order-Optimal Sequential 1-Bit Mean Estimation in General Tail Regimes
The paper develops an order-optimal adaptive 1-bit mean estimator for distributions with bounded k-th moments and proves a novel lower bound for the variance case.