  We tackle the modeling of threshold exceedances in asymptotically independent
stochastic processes by constructions based on Laplace random fields. These are
defined as Gaussian random fields scaled with a stochastic variable following
an exponential distribution. This framework yields useful asymptotic properties
while remaining statistically convenient. Univariate distribution tails are of
the half exponential type and are part of the limiting generalized Pareto
distributions for threshold exceedances. After normalizing marginal tail
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 for Laplace fields 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 terms of Akaike's criterion. In this specific application we
fit the well-adapted Weibull distribution as univariate tail model, such that
the normalization of univariate tail distributions can be done through a simple
power transformation of data.

Methodology;Other Statistics