An information-theoretic lower bound in time-uniform estimation
CoRR(2024)
摘要
We present an information-theoretic lower bound for the problem of parameter
estimation with time-uniform coverage guarantees. Via a new a reduction to
sequential testing, we obtain stronger lower bounds that capture the hardness
of the time-uniform setting. In the case of location model estimation, logistic
regression, and exponential family models, our Ω(√(n^-1loglog
n)) lower bound is sharp to within constant factors in typical settings.
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