In most prediction and estimation situations, scientists consider various statistical models for the same problem, and naturally want to select amongst the best. Hansen et al. (2011) provide a powerful solution to this problem by the so-called model confidence set, a subset of the original set of available models that contains the best models with a given level of confidence. Importantly, model confidence sets respect the underlying selection uncertainty by being flexible in size. However, they presuppose a fixed sample size which stands in contrast to the fact that model selection and forecast evaluation are inherently sequential tasks where we successively collect new data and where the decision to continue or conclude a study may depend on the previous outcomes. In this article, we extend model confidence sets sequentially over time by relying on sequential testing methods. Recently, e-processes and confidence sequences have been introduced as new, safe methods for assessing statistical evidence. Sequential model confidence sets allow to continuously monitor the models' performances and come with time-uniform, nonasymptotic coverage guarantees.

翻译：在大多数预测与估计场景中，研究者通常会针对同一问题考虑多种统计模型，并自然希望从中筛选出最优模型。Hansen等人（2011）通过所谓的模型置信集为该问题提供了强有力的解决方案——这是一个原始可用模型集合的子集，能够以给定置信水平包含最优模型。重要之处在于，模型置信集通过尺寸灵活性充分尊重了底层选择的不确定性。然而，这些方法预设了固定样本量，这与模型选择与预测评估本质上属于序贯任务的现实相矛盾——在此类任务中，我们需要持续收集新数据，而是否继续研究或终止研究的决策往往取决于先前的观测结果。本文通过依赖序贯检验方法，将模型置信集在时间维度上进行了序贯扩展。近期提出的e-过程与置信序列作为评估统计证据的新型安全方法被引入。时序模型置信集能够持续监测模型表现，并具有时间一致、非渐近的覆盖保证。