It is natural, when contemplating an historical record of events, to base a simple estimator of the event‐rate on that recent part of the record where the recording probability is thought to be effectively 1. After all, this avoids the downward bias which would be incurred by ‘overshooting’ into a time where the recording probability was less than 1. However, there is a trade‐off, because overshooting also decreases the variance of the event‐rate estimator. In fact, it is always beneficial to overshoot, measured in terms of the risk of the estimator. Perhaps surprisingly, the beneficial overshoot can often be large. This paper provides these theoretical results, along with some illustrations.

中文翻译：

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从不可靠的历史记录中估算事件发生率

在考虑事件的历史记录时，很自然的是，将事件率的简单估计值基于记录的最近部分，该记录的记录概率被认为是有效的1。毕竟，这避免了向下的偏见在记录概率小于1的时间内“超调”会引起这种情况。但是，这是一个折衷方案，因为超调也会减小事件率估计量的方差。实际上，以估算器的风险衡量，过冲总是有益的。也许令人惊讶的是，有益的超调通常可能很大。本文提供了这些理论结果以及一些说明。