On Parametric and Nonparametric Estimation of the Dependence Function in Multivariate Extremes

• Activity Number: 591
• Type: Topic Contributed
• Date/Time: Wednesday, August 12, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Sabrina Vettori* and Raphael Huser and Marc Genton
• Companies: KAUST and KAUST and KAUST
• Keywords: Asymmetric logistic family ; Bernstein-Bezier polynomial ; componentwise maxima ; convexity ; non-parametric and parametric estimators ; Pickands dependence function

Abstract

In a wide range of environmental applications it is of interest to model the behaviour of several variables at high levels, such as extremes of natural phenomena observed at distinct locations. Various non-parametric and parametric estimators of the dependence structure for multivariate maxima have been proposed. In this paper we investigate, through an extensive simulation study, the performance of some of these estimators under different dependence scenarios, focusing on the comparison between non-parametric and parametric approaches. In particular, we assess the performance of several non-parametric estimators, considering two different ways to make them satisfy the necessary constraints: either by naive modifications proposed in the literature or by projecting them onto the subspace of valid dependence functions. Non-parametric methods are then compared with parametric methods within the asymmetric logistic family of dependence structures.