Bias-corrected and robust estimation of the bivariate stable tail dependence function

Mikael Escobar-Bach, Yuri Goegebeur (), Armelle Guillou and Alexandre You
Additional contact information
Mikael Escobar-Bach: University of Southern Denmark
Yuri Goegebeur: University of Southern Denmark
Armelle Guillou: Avancée, UMR 7501, Université de Strasbourg et CNRS
Alexandre You: Direction Technique

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2017, vol. 26, issue 2, No 3, 284-307

Abstract: Abstract The stable tail dependence function gives a full characterisation of the extremal dependence between two or more random variables. In this paper, we propose an estimator for this function which is robust against outliers in the sample. The estimator is derived from a bivariate second-order tail model together with a proper transformation of the bivariate observations, and its asymptotic properties are studied under some suitable regularity conditions. Our estimation procedure depends on two parameters: $$\alpha $$ α , which controls the trade-off between efficiency and robustness of the estimator, and a second-order parameter $$\tau $$ τ , which can be replaced by a fixed value or by an estimate. In case where $$\tau $$ τ has been replaced by the true value or by an external consistent estimator, our robust estimator is asymptotically unbiased, whereas in case where $$\tau $$ τ is mis-specified, one loses this property, but still our estimator performs quite well with respect to bias. The finite sample performance of our robust and bias-corrected estimator of the stable tail dependence function is examined on a simulation study involving uncontaminated and contaminated samples. In particular, its behavior is illustrated for different values of the pair $$(\alpha , \tau )$$ ( α , τ ) and is compared with alternative estimators from the extreme value literature.

Keywords: Multivariate extreme value statistics; Stable tail dependence function; Robustness; Bias-correction; 62G05; 62G20; 62G32 (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://link.springer.com/10.1007/s11749-016-0511-5 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:testjl:v:26:y:2017:i:2:d:10.1007_s11749-016-0511-5

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/11749/PS2

DOI: 10.1007/s11749-016-0511-5

Access Statistics for this article

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research is currently edited by Alfonso Gordaliza and Ana F. Militino

More articles in TEST: An Official Journal of the Spanish Society of Statistics and Operations Research from Springer, Sociedad de Estadística e Investigación Operativa
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().