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Statistical inference for max‐stable processes in space and time
Author(s) -
Davis Richard A.,
Klüppelberg Claudia,
Steinkohl Christina
Publication year - 2013
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12012
Subject(s) - pointwise , mathematics , pairwise comparison , statistical inference , inference , consistency (knowledge bases) , maxima , estimator , representation (politics) , limit (mathematics) , maxima and minima , random field , gaussian process , gaussian , statistical physics , statistics , computer science , discrete mathematics , mathematical analysis , artificial intelligence , art , physics , quantum mechanics , performance art , politics , political science , law , art history
Summary 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.