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research article

Multivariate extremes over a random number of observations

Hashorva, Enkelejd
•
Padoan, Simone A.
•
Rizzelli, Stefano  
2021
Scandinavian Journal Of Statistics

The classical multivariate extreme-value theory concerns the modeling of extremes in a multivariate random sample, suggesting the use of max-stable distributions. In this work, the classical theory is extended to the case where aggregated data, such as maxima of a random number of observations, are considered. We derive a limit theorem concerning the attractors for the distributions of the aggregated data, which boil down to a new family of max-stable distributions. We also connect the extremal dependence structure of classical max-stable distributions and that of our new family of max-stable distributions. Using an inversion method, we derive a semiparametric composite-estimator for the extremal dependence of the unobservable data, starting from a preliminary estimator of the extremal dependence of the aggregated data. Furthermore, we develop the large-sample theory of the composite-estimator and illustrate its finite-sample performance via a simulation study.

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Type
research article
DOI
10.1111/sjos.12463
Web of Science ID

WOS:000552748400001

Author(s)
Hashorva, Enkelejd
•
Padoan, Simone A.
•
Rizzelli, Stefano  
Date Issued

2021

Publisher

WILEY

Published in
Scandinavian Journal Of Statistics
Volume

48

Issue

3

Start page

845

End page

880

Subjects

Statistics & Probability

•

Mathematics

•

extremal dependence

•

extreme-value copula

•

inverse problem

•

multivariate max-stable distribution

•

nonparametric estimation

•

pickands dependence function

•

nonparametric-estimation

•

dependence

•

inference

Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
STAT  
Available on Infoscience
August 12, 2020
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/170798
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