Publication result detail

Improved interexceedance-times-based estimator of the extremal index using truncated distribution

HOLEŠOVSKÝ, J.; FUSEK, M.

Original Title

Improved interexceedance-times-based estimator of the extremal index using truncated distribution

English Title

Improved interexceedance-times-based estimator of the extremal index using truncated distribution

Type

WoS Article

Original Abstract

The extremal index is an important parameter in the characterization of extreme values of a stationary sequence. This paper presents a novel approach to estimation of the extremal index based on truncation of interexceedance times. The truncated estimator based on the maximum likelihood method is derived together with its first-order bias. The estimator is further improved using penultimate approximation to the limiting mixture distribution. In order to assess the performance of the proposed estimator, a simulation study is carried out for various stationary processes satisfying the local dependence condition $D^{(k)}(u_n)$. An application to daily maximum temperatures at Uccle, Belgium, is also presented.

English abstract

The extremal index is an important parameter in the characterization of extreme values of a stationary sequence. This paper presents a novel approach to estimation of the extremal index based on truncation of interexceedance times. The truncated estimator based on the maximum likelihood method is derived together with its first-order bias. The estimator is further improved using penultimate approximation to the limiting mixture distribution. In order to assess the performance of the proposed estimator, a simulation study is carried out for various stationary processes satisfying the local dependence condition $D^{(k)}(u_n)$. An application to daily maximum temperatures at Uccle, Belgium, is also presented.

Keywords

Extremal index; Extreme value theory; Truncation; Clusters

Key words in English

Extremal index; Extreme value theory; Truncation; Clusters

Authors

HOLEŠOVSKÝ, J.; FUSEK, M.

RIV year

2023

Released

24.06.2022

Publisher

Springer

Location

Berlin

ISBN

1386-1999

Periodical

Extremes

Volume

25

Number

4

State

United States of America

Pages from

695

Pages to

720

Pages count

26

URL

https://link.springer.com/article/10.1007/s10687-022-00444-8

BibTex

@article{BUT178357,
  author="Jan {Holešovský} and Michal {Fusek}",
  title="Improved interexceedance-times-based estimator of the extremal index using truncated distribution",
  journal="Extremes",
  year="2022",
  volume="25",
  number="4",
  pages="695--720",
  doi="10.1007/s10687-022-00444-8",
  issn="1386-1999",
  url="https://link.springer.com/article/10.1007/s10687-022-00444-8"
}