Conditioned limit laws for inverted max-stable processes

JOURNAL OF MULTIVARIATE ANALYSIS

卷:150

Article

Papastathopoulos, Ioannis^1,2,3  Tawn, Jonathan A.⁴ 

[1] Univ Edinburgh, Sch Math, Edinburgh EH9 3FD, Midlothian, Scotland

[2] Univ Edinburgh, Maxwell Inst, Edinburgh EH9 3FD, Midlothian, Scotland

[3] British Lib, Alan Turing Inst Data Sci, London NW1 2DB, England

[4] Univ Lancaster, Dept Math & Stat, Lancaster LA1 4YF, England

关键词: Asymptotic independence;    Brown-Resnick process;    Conditional extremes;    Extremal-t process;    Husler-Reiss copula;    Inverted max-stable distribution;    Spatial extremes;   

DOI  :  10.1016/j.jmva.2016.06.001

来源: Elsevier

【 摘 要 】

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-t, 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. (C) 2016 Elsevier Inc. All rights reserved.

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