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arXiv · 2402.08794

An information-theoretic lower bound in time-uniform estimation

John C. Duchi·Saminul Haque
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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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John C. Duchi, Saminul Haque. 2024-02-13. An information-theoretic lower bound in time-uniform estimation. https://arxiv.org/abs/2402.08794

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