A class of goodness-of-fit tests for spatial extremes models based on max-stable processes

Details A class of goodness-of-fit tests for spatial extremes models based on max-stable processes A class of goodness-of-fit tests for spatial extremes models based on max-stable processes

2012-02-02

arxiv.org/abs/1202.0514v1

Statistics

Methodology

32 pages, 4 figures, 7 tables

Scientific paper

Parametric max-stable processes are increasingly used to model spatial extremes. Starting from the fact that the dependence structure of a simple max-stable process is completely characterized by an extreme-value copula, a class of goodness-of-fit tests is proposed based on the comparison between a nonparametric and a parametric estimator of the corresponding unknown multivariate Pickands dependence function. Because of the high-dimensional setting under consideration, these functional estimators are only compared at a specific set of points at which they coincide, up to a multiplicative constant, with estimators of the extremal coefficients. The nonparametric estimators of the Pickands dependence function used in this work are those recently studied by Gudendorf and Segers. The parametric estimators rely on the use of the composite pseudo-likelihood which extends the concept of composite likelihood to a rank-based context. Approximate p-values for the resulting margin-free tests are obtained by means of a one- or two-level parametric bootstrap. Conditions for the asymptotic validity of these resampling procedures are given based on the work of Genest and R\'emillard. The finite-sample performance of the tests is investigated in dimensions 20 and 40 under the Smith and the Schlather models for three spatial dependence scenarios. An application of the tests to Swiss extreme precipitation data is finally presented.

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