“Forecasting Records by Maximum Likelihood”, 1988 ():
A maximum likelihood method of fitting a model to a series of records is proposed, using ideas from the analysis of censored data to construct a likelihood function based on observed records.
This method is tried out by fitting several models to series of athletics records for mile and marathon races. A form of residual analysis is proposed for testing the models. Forecasting consequences are also considered.
In the case of mile records, a steady linear improvement since 1931 is found. The marathon data are harder to interpret, with a steady improvement until 1965 with only slight improvement in world records since then.
In both cases, the normal distribution appears at least as good as extreme-value distributions for the distribution of annual best performances. Short-term forecasts appear satisfactory, but serious reservations are expressed about using regression-type methods to predict long-term performance limits.
[Keywords: athletics records, censored data, generalized extreme-value distribution, Gumbel distribution, inference for stochastic processes]