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    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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Conditioned limit laws for inverted max-stable processes

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Conditioned limit laws for inverted max-stable processes. / Papastathopoulos, Ioannis; Tawn, Jonathan Angus.
In: Journal of Multivariate Analysis, Vol. 150, 09.2016, p. 214-228.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Harvard

Papastathopoulos, I & Tawn, JA 2016, 'Conditioned limit laws for inverted max-stable processes', Journal of Multivariate Analysis, vol. 150, pp. 214-228. https://doi.org/10.1016/j.jmva.2016.06.001

APA

Papastathopoulos, I., & Tawn, J. A. (2016). Conditioned limit laws for inverted max-stable processes. Journal of Multivariate Analysis, 150, 214-228. https://doi.org/10.1016/j.jmva.2016.06.001

Vancouver

Papastathopoulos I, Tawn JA. Conditioned limit laws for inverted max-stable processes. Journal of Multivariate Analysis. 2016 Sept;150:214-228. Epub 2016 Jun 22. doi: 10.1016/j.jmva.2016.06.001

Author

Papastathopoulos, Ioannis ; Tawn, Jonathan Angus. / Conditioned limit laws for inverted max-stable processes. In: Journal of Multivariate Analysis. 2016 ; Vol. 150. pp. 214-228.

Bibtex

@article{ed7a115018234bce85e5f5cfd0f304b9,
title = "Conditioned limit laws for inverted max-stable processes",
abstract = "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.",
keywords = "Asymptotic independence, Brown–Resnick process, Conditional extremes, Extremal-tt process, H{\"u}sler–Reiss copula, Inverted max-stable distribution, Spatial extremes",
author = "Ioannis Papastathopoulos and Tawn, {Jonathan Angus}",
note = "This is the author{\textquoteright}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",
year = "2016",
month = sep,
doi = "10.1016/j.jmva.2016.06.001",
language = "English",
volume = "150",
pages = "214--228",
journal = "Journal of Multivariate Analysis",
issn = "0047-259X",
publisher = "Academic Press Inc.",

}

RIS

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 -