Statistical inference for max‐stable processes in space and time

By Richard A. Davis, Claudia Klüppelberg, C. Steinkohl. 2012

87 citations recorded by the source corpus.

Max‐stable processes have proved to be useful for the statistical modelling of spatial extremes. Several families of max‐stable random fields have been proposed in the literature. One such representation is based on a limit of normalized and rescaled pointwise maxima of stationary Gaussian processes that was first introduced by Kabluchko and co‐workers. This paper deals with statistical inference for max‐stable space–time processes that are defined in an analogous fashion. We describe pairwise likelihood estimation, where the pairwise density of the process is used to estimate the model parameters. For regular grid observations we prove strong consistency and asymptotic normality of the parameter estimates as the joint number of spatial locations and time points tends to ∞. Furthermore, we discuss extensions to irregularly spaced locations. A simulation study shows that the method proposed works well for these models.

Subfields: Economics and Econometrics, Environmental Engineering, Finance

View Paper: https://www.semanticscholar.org/paper/6031d010a8f48578a18b631b9cdd416070331a28

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Citations in the corpus

Space–time modelling of extreme events (2012, background): “Davis et al. (2013a) show that this class of covariance functions satisfies a natural smoothness property at the origin, directly linked to the smoothness of the random field, and is therefore suitable for the modelling of physical processes such as rainfall.”
Max-stable processes for modelling extremes observed in space and time (2011, background): “In Davis, Klüppelberg and Steinkohl [12], composite likelihood methods for the estimation of the max-stable space-time processes introduced in this paper, are investigated.”
Non-Stationary Dependence Structures for Spatial Extremes (2014, background): “Similar asymptotic properties hold for mildly time-dependent processes (Davis et al., 2013; Huser and Davison, 2014) in which uncertainty may be assessed using block bootstrap.”