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Estimating event‐rates from unreliable historical records
Author(s) -
Rougier Jonathan
Publication year - 2021
Publication title -
journal of the royal statistical society: series a (statistics in society)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.103
H-Index - 84
eISSN - 1467-985X
pISSN - 0964-1998
DOI - 10.1111/rssa.12625
Subject(s) - estimator , event (particle physics) , overshoot (microwave communication) , variance (accounting) , statistics , econometrics , computer science , mathematics , economics , telecommunications , accounting , physics , quantum mechanics
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.