Detail publikačního výsledku

Statistical inference on the local dependence condition of extreme values in a stationary sequence

HOLEŠOVSKÝ, J.; FUSEK, M.

Originální název

Statistical inference on the local dependence condition of extreme values in a stationary sequence

Anglický název

Statistical inference on the local dependence condition of extreme values in a stationary sequence

Druh

Článek WoS

Originální abstrakt

The extremal index is an important characteristic measuring dependence of extreme values in a stationary series. Several new estimators that are mostly based on interexceedance times within the Peaks-over-Threshold model have been recently published. Nevertheless, in many cases these estimators rely on suitable choice of auxiliary parameters and/or are derived under assumptions that are related to validity of the local dependence condition $D^{(k)}(u_n)$. Although the determination of the correct order $k$ in the $D^{(k)}(u_n)$ condition can have major effect on the extremal index estimates, there are not many reliable methods available for this task. In this paper, we present various approaches to assessing validity of the $D^{(k)}(u_n)$ condition including a graphical diagnostics and propose several statistical tests. A simulation study is carried out to determine performance of the statistical tests, particularly the type I and type II errors.

Anglický abstrakt

The extremal index is an important characteristic measuring dependence of extreme values in a stationary series. Several new estimators that are mostly based on interexceedance times within the Peaks-over-Threshold model have been recently published. Nevertheless, in many cases these estimators rely on suitable choice of auxiliary parameters and/or are derived under assumptions that are related to validity of the local dependence condition $D^{(k)}(u_n)$. Although the determination of the correct order $k$ in the $D^{(k)}(u_n)$ condition can have major effect on the extremal index estimates, there are not many reliable methods available for this task. In this paper, we present various approaches to assessing validity of the $D^{(k)}(u_n)$ condition including a graphical diagnostics and propose several statistical tests. A simulation study is carried out to determine performance of the statistical tests, particularly the type I and type II errors.

Klíčová slova

Local dependence; extremal index; extreme value theory; clusters

Klíčová slova v angličtině

Local dependence; extremal index; extreme value theory; clusters

Autoři

HOLEŠOVSKÝ, J.; FUSEK, M.

Vydáno

28.07.2025

Nakladatel

Springer

ISSN

1386-1999

Periodikum

Extremes

Svazek

28

Číslo

3

Stát

Spojené státy americké

Strany od

557

Strany do

578

Strany počet

22

URL

https://link.springer.com/article/10.1007/s10687-025-00513-8

Plný text v Digitální knihovně

http://hdl.handle.net/11012/255408

BibTex

@article{BUT197986,
  author="Jan {Holešovský} and Michal {Fusek}",
  title="Statistical inference on the local dependence condition of extreme values in a stationary sequence",
  journal="Extremes",
  year="2025",
  volume="28",
  number="3",
  pages="557--578",
  doi="10.1007/s10687-025-00513-8",
  issn="1386-1999",
  url="https://link.springer.com/article/10.1007/s10687-025-00513-8"
}

Dokumenty

s10687-025-00513-8