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：本文针对具有时间一致覆盖保证的参数估计问题，提出了一个信息论下界。通过一种新的归约到序列检验的方法，我们获得了更强的下界，该下界捕捉了时间一致设定下的困难性。在位置模型估计、逻辑回归和指数族模型的情形中，我们的$\Omega(\sqrt{n^{-1}\log \log n})$下界在典型设定下是精确的，最多相差常数因子。