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An information-theoretic lower bound in time-uniform estimation (2402.08794v2)
Published 13 Feb 2024 in cs.IT, math.IT, math.ST, and stat.TH
Abstract: 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 $\Omega(\sqrt{n{-1}\log \log n})$ lower bound is sharp to within constant factors in typical settings.
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