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We develop methods, based on extreme value theory, for analysing observationsin the tails of longitudinal data, i.e., a data set consisting of a largenumber of short time series, which are typically irregularly andnon-simultaneously sampled, yet have some commonality in the structure of eachseries and exhibit independence between time series. Extreme value theory hasnot been considered previously for the unique features of longitudinal data.Across time series the data are assumed to follow a common generalised Paretodistribution, above a high threshold. To account for temporal dependence ofsuch data we require a model to describe (i) the variation between thedifferent time series properties, (ii) the changes in distribution over time,and (iii) the temporal dependence within each series. Our methodology has theflexibility to capture both asymptotic dependence and asymptotic independence,with this characteristic determined by the data. Bayesian inference is usedgiven the need for inference of parameters that are unique to each time series.Our novel methodology is illustrated through the analysis of data from eliteswimmers in the men's 100m breaststroke. Unlike previous analyses ofpersonal-best data in this event, we are able to make inference about thecareers of individual swimmers - such as the probability an individual willbreak the world record or swim the fastest time next year.

A framework for statistical modelling of the extremes of longitudinal data, applied to elite swimming