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.

翻译：我们针对具有时间一致覆盖保证的参数估计问题，提出了一种信息论下界。通过一种新的归约至序贯检验方法，我们获得了更强的下界，以刻画时间一致设定的难度。在位置模型估计、逻辑回归以及指数族模型的场景中，我们的 $\Omega(\sqrt{n^{-1}\log \log n})$ 下界在典型设定下常数因子范围内是紧的。