Non-Linear Models for Extremal Dependence

Journal of Multivariate Analysis, Volume 159, April 2017, Pages 49-66

32 Pages Posted: 11 Sep 2016 Last revised: 6 Jul 2017

See all articles by Linda Mhalla

Linda Mhalla

University of Lausanne, School of Economics and Business Administration (HEC Lausanne); University of Geneva, Geneva School of Economics and Management, Research Center for Statistics; HEC Montreal - Department of Decision Sciences

Valérie Chavez-Demoulin

University of Lausanne - School of Economics and Business Administration (HEC-Lausanne)

Philippe Naveau

Laboratoire des Sciences du Climat et de l'Environnement (LSCE)

Date Written: September 8, 2016

Abstract

The dependence structure of max-stable random vectors can be characterized by their Pickands dependence function. In many applications, the extremal dependence measure varies with covariates. We develop a flexible, semi-parametric method for the estimation of non-stationary multivariate Pickands dependence functions. The proposed construction is based on an accurate max-projection allowing to pass from the multivariate to the univariate setting and to rely on the generalized additive modeling framework. In the bivariate case, the resulting estimator of the Pickands function is regularized using constrained median smoothing B-splines, and bootstrap variability bands are constructed. In higher dimensions, we tailor our approach to the estimation of the extremal coefficient. An extended simulation study suggests that our estimator performs well and is competitive with the standard estimators in the absence of covariates. We apply the new methodology to a temperature dataset in the U.S. where the extremal dependence is linked to time and altitude.

Keywords: Extreme value theory, Generalized additive models, Max-stable random vectors, Non-stationarity, Pickands function, Semi-parametric models, Temperature data.

Suggested Citation

Mhalla, Linda and Chavez-Demoulin, Valérie and Naveau, Philippe, Non-Linear Models for Extremal Dependence (September 8, 2016). Journal of Multivariate Analysis, Volume 159, April 2017, Pages 49-66, Available at SSRN: https://ssrn.com/abstract=2836587 or http://dx.doi.org/10.2139/ssrn.2836587

Linda Mhalla (Contact Author)

University of Lausanne, School of Economics and Business Administration (HEC Lausanne) ( email )

Lausanne, Vaud
Switzerland

HEC Montreal - Department of Decision Sciences ( email )

3000 Côte-Sainte-Catherine Road
Montreal, QC H2S1L4
Canada

University of Geneva, Geneva School of Economics and Management, Research Center for Statistics ( email )

Geneva
Switzerland
+41 379 82 12 (Phone)

Valérie Chavez-Demoulin

University of Lausanne - School of Economics and Business Administration (HEC-Lausanne) ( email )

Unil Dorigny, Batiment Anthropole
Lausanne, 1015
Switzerland

HOME PAGE: http://https://www.hec.unil.ch/people/vchavez&vue=contact&set_language=en&cl=en

Philippe Naveau

Laboratoire des Sciences du Climat et de l'Environnement (LSCE) ( email )

Point Courrier 129
Gif-Sur-Yvette, 91191
France

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