Trends in sample extremes are of interest in many contexts, an example being environmental statistics. Parametric models are often used to model trends in such data, but they may not be suitable for exploratory data analysis. This paper outlines a semiparametric approach to smoothing sample extremes, based on local polynomial ®tting of the generalized extreme value distribution and related models. The uncertainty of ®ts is assessed by using resampling methods. The methods are applied to data on extreme temperatures and on record times for the women's 3000 m race.

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SUMMARYA class of doubly stochastic Poisson processes, which is termed a Markov-modulated Poisson process, is studied. The maximum likelihood method is used to make inferences about the Markov-modulated Poisson process. Expressions are derived for the likelihood function and for second-order properties of both counts and intervals. A simple two-state model is applied to a set of exposure data and to simulated data. Bivariate generalization of this process is also studied.

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