Conditioned limit laws for inverted max-stable processes

Papastathopoulos, Ioannis and Tawn, Jonathan Angus (2016) Conditioned limit laws for inverted max-stable processes. Journal of Multivariate Analysis, 150. pp. 214-228. ISSN 0047-259X

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Max-stable processes are widely used to model spatial extremes. These processes exhibit asymptotic dependence meaning that the large values of the process can occur simultaneously over space. Recently, inverted max-stable processes have been proposed as an important new class for spatial extremes which are in the domain of attraction of a spatially independent max-stable process but instead they cover the broad class of asymptotic independence. To study the extreme values of such processes we use the conditioned approach to multivariate extremes that characterises the limiting distribution of appropriately normalised random vectors given that at least one of their components is large. The current statistical methods for the conditioned approach are based on a canonical parametric family of location and scale norming functions. We study broad classes of inverted max-stable processes containing processes linked to the widely studied max-stable models of Brown-Resnick and extremal-tt, and identify conditions for the normalisations to either belong to the canonical family or not. Despite such differences at an asymptotic level, we show that at practical levels, the canonical model can approximate well the true conditional distributions.

Item Type:
Journal Article
Journal or Publication Title:
Journal of Multivariate Analysis
Additional Information:
This is the author’s version of a work that was accepted for publication in Journal of Multivariate Analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Multivariate Analysis, 150, 2016 DOI: 10.1016/j.jmva.2016.06.001
Uncontrolled Keywords:
?? asymptotic independencebrown–resnick processconditional extremesextremal-tt processhüsler–reiss copulainverted max-stable distributionspatial extremesstatistics and probabilitystatistics, probability and uncertaintynumerical analysis ??
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Deposited On:
27 Jun 2016 08:28
Last Modified:
18 Dec 2023 01:39