Modeling asymptotically independent spatial extremes based on Laplace random fields

We tackle the modeling of threshold exceedances in asymptotically independent stochastic processes by constructions based on Laplace random fields. Defined as mixtures of Gaussian random fields with an exponential variable embedded for the variance, these processes possess useful asymptotic properties while remaining statistically convenient. Univariate Laplace distribution tails are part of the limiting generalized Pareto distributions for threshold exceedances. After normalizing marginal distributions in data, a standard Laplace field can be used to capture spatial dependence among extremes. Asymptotic properties of Laplace fields are explored and compared to the classical framework of asymptotic dependence. Multivariate joint tail decay rates are slower than for Gaussian fields with the same covariance structure; hence they provide more conservative estimates of very extreme joint risks while maintaining asymptotic independence. Statistical inference is illustrated on extreme wind gusts in the Netherlands where a comparison to the Gaussian dependence model shows a better goodness-of-fit. In this application we fit the well-adapted Weibull distribution, closely related to the Laplace distribution, as univariate tail model.