论文标题
最小值，没有固定样本量假设
Minimax rates without the fixed sample size assumption
论文作者
论文摘要
我们概括了最小值收敛速率的概念。与标准定义相反，我们不假定样本量已提前固定。允许不同的样本量导致时型最小速率和估计器。这些可以是基于所有样本量的最坏情况，或者基于所有停止时间最差的案例，可以是强烈的对抗性。我们表明，标准和时间刺激的速率通常会大多在对数因素上有所不同，而对于某些（我们都猜想）指数族的家族，它们的差异与迭代的对数因子完全不同。在许多情况下，可以说更自然的时间努力。例如，它们使我们能够同时获得强大的模型选择一致性和最佳估计率，从而避免了“ AIC-BIC困境”。
We generalize the notion of minimax convergence rate. In contrast to the standard definition, we do not assume that the sample size is fixed in advance. Allowing for varying sample size results in time-robust minimax rates and estimators. These can be either strongly adversarial, based on the worst-case over all sample sizes, or weakly adversarial, based on the worst-case over all stopping times. We show that standard and time-robust rates usually differ by at most a logarithmic factor, and that for some (and we conjecture for all) exponential families, they differ by exactly an iterated logarithmic factor. In many situations, time-robust rates are arguably more natural to consider. For example, they allow us to simultaneously obtain strong model selection consistency and optimal estimation rates, thus avoiding the "AIC-BIC dilemma".
