Rights statement: 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
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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Conditioned limit laws for inverted max-stable processes
AU - Papastathopoulos, Ioannis
AU - Tawn, Jonathan Angus
N1 - 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
PY - 2016/9
Y1 - 2016/9
N2 - 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.
AB - 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.
KW - Asymptotic independence
KW - Brown–Resnick process
KW - Conditional extremes
KW - Extremal-tt process
KW - Hüsler–Reiss copula
KW - Inverted max-stable distribution
KW - Spatial extremes
U2 - 10.1016/j.jmva.2016.06.001
DO - 10.1016/j.jmva.2016.06.001
M3 - Journal article
VL - 150
SP - 214
EP - 228
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
SN - 0047-259X
ER -