An asymptotically unbiased minimum density power divergence estimator for the Pareto-tail index

Goedele Dierckx, Yuri Goegebeur, Armelle Guillou

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

We introduce a robust and asymptotically unbiased estimator for the tail index of Pareto-type distributions. The estimator is obtained by fitting the extended Pareto distribution to the relative excesses over a high threshold with the minimum density power divergence criterion. Consistency and asymptotic normality of the estimator is established under a second order condition on the distribution underlying the data, and for intermediate sequences of upper order statistics. The finite sample properties of the proposed estimator and some alternatives from the extreme value literature are evaluated by a small simulation experiment involving both uncontaminated and contaminated samples. (C) 2013 Elsevier Inc. All rights reserved.
Original languageEnglish
JournalJournal of Multivariate Analysis
Volume121
Pages (from-to)70-86
ISSN0047-259X
DOIs
Publication statusPublished - 2013

Fingerprint

Power Divergence
Tail Index
Pareto
Statistics
Estimator
Second-order Conditions
Pareto Distribution
Experiments
Unbiased estimator
Extreme Values
Order Statistics
Asymptotic Normality
Simulation Experiment
Excess
Alternatives
Tail index
Divergence

Keywords

  • Pareto-type distribution Tail index Bias-correction Density power divergence ROBUST DISTRIBUTIONS THRESHOLD EXPONENT

Cite this

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title = "An asymptotically unbiased minimum density power divergence estimator for the Pareto-tail index",
abstract = "We introduce a robust and asymptotically unbiased estimator for the tail index of Pareto-type distributions. The estimator is obtained by fitting the extended Pareto distribution to the relative excesses over a high threshold with the minimum density power divergence criterion. Consistency and asymptotic normality of the estimator is established under a second order condition on the distribution underlying the data, and for intermediate sequences of upper order statistics. The finite sample properties of the proposed estimator and some alternatives from the extreme value literature are evaluated by a small simulation experiment involving both uncontaminated and contaminated samples. (C) 2013 Elsevier Inc. All rights reserved.",
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pages = "70--86",
journal = "Journal of Multivariate Analysis",
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An asymptotically unbiased minimum density power divergence estimator for the Pareto-tail index. / Dierckx, Goedele; Goegebeur, Yuri; Guillou, Armelle.

In: Journal of Multivariate Analysis, Vol. 121, 2013, p. 70-86.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - An asymptotically unbiased minimum density power divergence estimator for the Pareto-tail index

AU - Dierckx, Goedele

AU - Goegebeur, Yuri

AU - Guillou, Armelle

PY - 2013

Y1 - 2013

N2 - We introduce a robust and asymptotically unbiased estimator for the tail index of Pareto-type distributions. The estimator is obtained by fitting the extended Pareto distribution to the relative excesses over a high threshold with the minimum density power divergence criterion. Consistency and asymptotic normality of the estimator is established under a second order condition on the distribution underlying the data, and for intermediate sequences of upper order statistics. The finite sample properties of the proposed estimator and some alternatives from the extreme value literature are evaluated by a small simulation experiment involving both uncontaminated and contaminated samples. (C) 2013 Elsevier Inc. All rights reserved.

AB - We introduce a robust and asymptotically unbiased estimator for the tail index of Pareto-type distributions. The estimator is obtained by fitting the extended Pareto distribution to the relative excesses over a high threshold with the minimum density power divergence criterion. Consistency and asymptotic normality of the estimator is established under a second order condition on the distribution underlying the data, and for intermediate sequences of upper order statistics. The finite sample properties of the proposed estimator and some alternatives from the extreme value literature are evaluated by a small simulation experiment involving both uncontaminated and contaminated samples. (C) 2013 Elsevier Inc. All rights reserved.

KW - Pareto-type distribution Tail index Bias-correction Density power divergence ROBUST DISTRIBUTIONS THRESHOLD EXPONENT

U2 - 10.1016/j.jmva.2013.06.011

DO - 10.1016/j.jmva.2013.06.011

M3 - Journal article

VL - 121

SP - 70

EP - 86

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

SN - 0047-259X

ER -