An information-theoretic lower bound in time-uniform estimation
<|reference_start|>An information-theoretic lower bound in time-uniform estimation: 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.<|reference_end|>
@article{duchi2024an,
    title={An information-theoretic lower bound in time-uniform estimation},
    author={John C. Duchi and Saminul Haque},
    journal={arXiv preprint arXiv:2402.08794},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.08794},
    primaryClass={cs.IT math.IT math.ST stat.TH}
}