Iterative estimation of the extreme value index

Samuel Müller; Jürg Hüsler

doi:10.1007/s11009-005-1487-x

Iterative estimation of the extreme value index

Samuel Müller^*, Jürg Hüsler

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

Let {X_n, n ≥ 1} be a sequence of independent random variables with common continuous distribution function F having finite and unknown upper endpoint. A new iterative estimation procedure for the extreme value index γ is proposed and one implemented iterative estimator is investigated in detail, which is asymptotically as good as the uniform minimum varianced unbiased estimator in an ideal model. Moreover, the superiority of the iterative estimator over its non iterated counterpart in the non asymptotic case is shown in a simulation study.

Original language	English
Pages (from-to)	139-148
Number of pages	10
Journal	Methodology and Computing in Applied Probability
Volume	7
Issue number	2
DOIs	https://doi.org/10.1007/s11009-005-1487-x
Publication status	Published - Jun 2005
Externally published	Yes

Keywords

extreme value theory
tail index estimation
iterative estimator

Access to Document

10.1007/s11009-005-1487-x

Cite this

@article{8602eed339594bea81608e9f0f80d32f,

title = "Iterative estimation of the extreme value index",

abstract = "Let {Xn, n ≥ 1} be a sequence of independent random variables with common continuous distribution function F having finite and unknown upper endpoint. A new iterative estimation procedure for the extreme value index γ is proposed and one implemented iterative estimator is investigated in detail, which is asymptotically as good as the uniform minimum varianced unbiased estimator in an ideal model. Moreover, the superiority of the iterative estimator over its non iterated counterpart in the non asymptotic case is shown in a simulation study.",

keywords = "extreme value theory, tail index estimation, iterative estimator",

author = "Samuel M{\"u}ller and J{\"u}rg H{\"u}sler",

year = "2005",

month = jun,

doi = "10.1007/s11009-005-1487-x",

language = "English",

volume = "7",

pages = "139--148",

journal = "Methodology and Computing in Applied Probability",

issn = "1387-5841",

publisher = "Springer, Springer Nature",

number = "2",

}

TY - JOUR

T1 - Iterative estimation of the extreme value index

AU - Müller, Samuel

AU - Hüsler, Jürg

PY - 2005/6

Y1 - 2005/6

N2 - Let {Xn, n ≥ 1} be a sequence of independent random variables with common continuous distribution function F having finite and unknown upper endpoint. A new iterative estimation procedure for the extreme value index γ is proposed and one implemented iterative estimator is investigated in detail, which is asymptotically as good as the uniform minimum varianced unbiased estimator in an ideal model. Moreover, the superiority of the iterative estimator over its non iterated counterpart in the non asymptotic case is shown in a simulation study.

AB - Let {Xn, n ≥ 1} be a sequence of independent random variables with common continuous distribution function F having finite and unknown upper endpoint. A new iterative estimation procedure for the extreme value index γ is proposed and one implemented iterative estimator is investigated in detail, which is asymptotically as good as the uniform minimum varianced unbiased estimator in an ideal model. Moreover, the superiority of the iterative estimator over its non iterated counterpart in the non asymptotic case is shown in a simulation study.

KW - extreme value theory

KW - tail index estimation

KW - iterative estimator

UR - http://www.scopus.com/inward/record.url?scp=22944474303&partnerID=8YFLogxK

U2 - 10.1007/s11009-005-1487-x

DO - 10.1007/s11009-005-1487-x

M3 - Article

AN - SCOPUS:22944474303

SN - 1387-5841

VL - 7

SP - 139

EP - 148

JO - Methodology and Computing in Applied Probability

JF - Methodology and Computing in Applied Probability

IS - 2

ER -

Iterative estimation of the extreme value index

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this