Generalized additive models for exceedances of high thresholds with an application to return level estimation for US wind gusts

Generalized additive model (GAM) forms offer a flexible approach to capturing marginal variation. Such forms are used here to represent distributional variation in extreme values and presented in terms of spatio-temporal variation, which is often evident in environmental processes. A two-stage procedure is proposed that identifies extreme values as exceedances of a high threshold, which is defined as a fixed quantile and estimated by quantile regression. Excesses of the threshold are modelled with the generalized Pareto distribution (GPD). GAM forms are adopted for the threshold and GPD parameters, and directly estimated—in particular smoothing parameters—by restricted maximum likelihood, which provides an objective and relatively fast method of inference. The GAM models are used to produce return level maps for extreme wind gust speeds over the United States, which show extreme quantiles of the distribution of annual maximum gust speeds.