Multivariate peaks over thresholds models

Rootzen, Holger and Segers, Johan and Wadsworth, Jennifer Lynne (2018) Multivariate peaks over thresholds models. Extremes, 21 (1). pp. 115-145. ISSN 1386-1999

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Abstract

Multivariate peaks over thresholds modelling based on generalized Pareto distributions has up to now only been used in few and mostly two-dimensional situations. This paper contributes theoretical understanding, models which can respect physical constraints, inference tools, and simulation methods to support routine use, with an aim at higher dimensions. We derive a general point process model for extreme episodes in data, and show how conditioning the distribution of extreme episodes on threshold exceedance gives four basic representations of the family of generalized Pareto distributions. The first representation is constructed on the real scale of the observations. The second one starts with a model on a standard exponential scale which is then transformed to the real scale. The third and fourth representations are re-formulations of a spectral representation proposed in A. Ferreira and L. de Haan [Bernoulli 20 (2014) 1717–1737]. Numerically tractable forms of densities and censored densities are found and give tools for flexible parametric likelihood inference. New simulation algorithms, explicit formulas for probabilities and conditional probabilities, and conditions which make the conditional distribution of weighted component sums generalized Pareto are derived.

Item Type:
Journal Article
Journal or Publication Title:
Extremes
Additional Information:
The final publication is available at Springer via http://dx.doi.org/10.1007/s10687-017-0294-4
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2613
Subjects:
ID Code:
85990
Deposited By:
Deposited On:
25 Apr 2017 12:42
Refereed?:
Yes
Published?:
Published
Last Modified:
16 Sep 2020 03:44