Modeling asymptotically independent spatial extremes based on Laplace random fields

By Thomas Opitz. 2015

67 citations recorded by the source corpus.

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.

Subfields: Environmental Engineering, Finance, Soil Science

View Paper: https://www.semanticscholar.org/paper/c7a6af046b009b51b8c4d1c6adedadb6f7752240

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Citations in the corpus

Modeling Spatial Processes with Unknown Extremal Dependence Class (2017, methodology): “This was used by Wadsworth and Tawn (2012), Opitz (2016) and Wadsworth et al.”
Factor Copula Models for Replicated Spatial Data (2015, background): “Another research direction is to include different types of common factors, for example models with multiplicative common factors (Opitz, 2016), which might be plausible in some applications, e.”
Time-series Extreme Event Forecasting with Neural Networks at Uber (2017, methodology): “Machine learning models are often used in conjunction with the univariate time-series models resulting in a bulky two-step process for addressing the extreme event forecasting problem (Opitz, 2015).”
Deep and Confident Prediction for Time Series at Uber (2017, background): “To more effectively deal with exogenous variables, a combination of univariate modeling and a machine learning model to handle residuals was introduced in [10].”
Bridging asymptotic independence and dependence in spatial extremes using Gaussian scale mixtures (2016, background): “…dependent submodels of the models that we propose are closely related to the elliptic Pareto process of Thibaud and Opitz (2015) while their asymptotically independent counterparts provide alternatives and more ﬂexible parametric extensions (Models 2 and 3) to the Laplace model of Opitz (2016).”