PARAMETRIC LIKELIHOOD INFERENCE FOR RECORD BREAKING PROBLEMS

In this paper we consider the analysis of record breaking data sets, w here only observations that exceed, or only those that fall below, the current extreme value are recorded. Example application areas include industrial stress testing, meteorological analysis, sporting and athl etic events, and oil and mining surveys. A closely related area is tha t of threshold modelling, where the observations are those that cross a certain threshold value. The inherent missing data structure present in these problems leads to likelihood functions that contain possibly high-dimensional integrals; rendering traditional maximum likelihood methods difficult or not feasible. Fortunately, we may obtain arbitrar ily accurate approximations to the likelihood function by iteratively applying Monte Carlo integration methods (Geyer & Thompson, 1992). Sub iteration using the Gibbs sampler may help to evaluate any multivariat e integrals encountered during this process. This approach can handle far more sophisticated parametric models than have been used previousl y in record breaking and threshold data contexts. In particular, the m ethodology allows for observations that are dependent and subject to m ean shifts over time. We present a numerical example involving records in Olympic high jump competition, where besides estimation we also ad dress related issues in model selection and prediction.