Robust and bias-corrected estimation of the probability of extreme failure sets

Christophe Dutang (), Yuri Goegebeur () and Armelle Guillou ()
Additional contact information
Christophe Dutang: LMM - Laboratoire Manceau de Mathématiques - UM - Le Mans Université
Yuri Goegebeur: IMADA - Department of Mathematics and Computer Science [Odense] - SDU - University of Southern Denmark
Armelle Guillou: IRMA - Institut de Recherche Mathématique Avancée - UNISTRA - Université de Strasbourg - CNRS - Centre National de la Recherche Scientifique

Post-Print from HAL

Abstract: In multivariate extreme value statistics, the estimation of probabilities of extreme failure sets is an important problem, with practical relevance for applications in several scientific disciplines. Some estimators have been introduced in the literature, though so far the typical bias issues that arise in application of extreme value methods and the non-robustness of such methods with respect to outliers were not addressed. We introduce a bias-corrected and robust estimator for small tail probabilities. The estimator is obtained from a second order model that is fitted to properly transformed bivariate observations by means of the minimum density power divergence technique. The asymptotic properties are derived under some mild regularity conditions and the finite sample performance is evaluated through an extensive simulation study. We illustrate the practical applicability of the method on a dataset from the actuarial context.

Keywords: failure set; bias-correction; tail dependence; robustness; tail quantile process (search for similar items in EconPapers)
Date: 2016-02
New Economics Papers: this item is included in nep-ecm
Note: View the original document on HAL open archive server: https://hal.science/hal-01616187
References: View references in EconPapers View complete reference list from CitEc
Citations:

Published in Sankhya A, 2016, 78 (1), pp.52-86. ⟨10.1007/s13171-015-0078-3⟩

Downloads: (external link)
https://hal.science/hal-01616187/document (application/pdf)

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:hal:journl:hal-01616187

DOI: 10.1007/s13171-015-0078-3

Access Statistics for this paper

More papers in Post-Print from HAL
Bibliographic data for series maintained by CCSD ().