Estimating event‐rates from unreliable historical records

Summary 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.