Smoothing sample extremes: The mixed model approach

Nonparametric regression for sample extremes can be performed using a variety of techniques. The penalized spline approach for the Poisson point process model is considered. The generalized linear mixed model representation for the spline model, with its Bayesian approach to inference, turns out to be a very flexible framework. Monte Carlo Markov chain algorithms are employed for exploration of the posterior distribution. The overall performance of the method is tested on simulated data. Two real data applications are also discussed for modeling trend of intensity of earthquakes in Italy and for assessing seasonality and short term trend of summer extreme temperatures in Milan, Italy.