Asymptotically unbiased estimation of the coefficient of tail dependence

Yuri Goegebeur, Armelle Guillou

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

Resumé

We introduce and study a class of weighted functional estimators for the coefficient of tail dependence in bivariate extreme value statistics. Asymptotic normality of these estimators is established under a second-order condition on the joint tail behaviour, some conditions on the weight function and for appropriately chosen sequences of intermediate order statistics. Asymptotically unbiased estimators are constructed by judiciously chosen linear combinations of weighted functional estimators, and variance optimality within this class of asymptotically unbiased estimators is discussed. The finite sample performance of some specific examples from our class of estimators and some alternatives from the recent literature are evaluated with a small simulation experiment.

OriginalsprogEngelsk
TidsskriftScandinavian Journal of Statistics
Vol/bind40
Sider (fra-til)174-189
ISSN0303-6898
DOI
StatusUdgivet - 2013

Fingeraftryk

Tail Dependence
Unbiased Estimation
Estimator
Unbiased estimator
Coefficient
Extreme Value Statistics
Second-order Conditions
Tail Behavior
Order Statistics
Asymptotic Normality
Weight Function
Simulation Experiment
Linear Combination
Optimality
Coefficients
Tail dependence
Alternatives
Class

Citer dette

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title = "Asymptotically unbiased estimation of the coefficient of tail dependence",
abstract = "We introduce and study a class of weighted functional estimators for the coefficient of tail dependence in bivariate extreme value statistics. Asymptotic normality of these estimators is established under a second-order condition on the joint tail behaviour, some conditions on the weight function and for appropriately chosen sequences of intermediate order statistics. Asymptotically unbiased estimators are constructed by judiciously chosen linear combinations of weighted functional estimators, and variance optimality within this class of asymptotically unbiased estimators is discussed. The finite sample performance of some specific examples from our class of estimators and some alternatives from the recent literature are evaluated with a small simulation experiment.",
keywords = "Bias-correction, Coefficient of tail dependence, Multivariate extremes, Second-order condition",
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Asymptotically unbiased estimation of the coefficient of tail dependence. / Goegebeur, Yuri; Guillou, Armelle.

I: Scandinavian Journal of Statistics, Bind 40, 2013, s. 174-189.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

TY - JOUR

T1 - Asymptotically unbiased estimation of the coefficient of tail dependence

AU - Goegebeur, Yuri

AU - Guillou, Armelle

PY - 2013

Y1 - 2013

N2 - We introduce and study a class of weighted functional estimators for the coefficient of tail dependence in bivariate extreme value statistics. Asymptotic normality of these estimators is established under a second-order condition on the joint tail behaviour, some conditions on the weight function and for appropriately chosen sequences of intermediate order statistics. Asymptotically unbiased estimators are constructed by judiciously chosen linear combinations of weighted functional estimators, and variance optimality within this class of asymptotically unbiased estimators is discussed. The finite sample performance of some specific examples from our class of estimators and some alternatives from the recent literature are evaluated with a small simulation experiment.

AB - We introduce and study a class of weighted functional estimators for the coefficient of tail dependence in bivariate extreme value statistics. Asymptotic normality of these estimators is established under a second-order condition on the joint tail behaviour, some conditions on the weight function and for appropriately chosen sequences of intermediate order statistics. Asymptotically unbiased estimators are constructed by judiciously chosen linear combinations of weighted functional estimators, and variance optimality within this class of asymptotically unbiased estimators is discussed. The finite sample performance of some specific examples from our class of estimators and some alternatives from the recent literature are evaluated with a small simulation experiment.

KW - Bias-correction

KW - Coefficient of tail dependence

KW - Multivariate extremes

KW - Second-order condition

U2 - 10.1111/j.1467-9469.2012.00800.x

DO - 10.1111/j.1467-9469.2012.00800.x

M3 - Journal article

VL - 40

SP - 174

EP - 189

JO - Scandinavian Journal of Statistics

JF - Scandinavian Journal of Statistics

SN - 0303-6898

ER -