Statistics and Computing

, Volume 28, Issue 3, pp 525–538 | Cite as

A comparison of dependence function estimators in multivariate extremes

Article

Abstract

Various nonparametric and parametric estimators of extremal dependence have been proposed in the literature. Nonparametric methods commonly suffer from the curse of dimensionality and have been mostly implemented in extreme-value studies up to three dimensions, whereas parametric models can tackle higher-dimensional settings. In this paper, we assess, through a vast and systematic simulation study, the performance of classical and recently proposed estimators in multivariate settings. In particular, we first investigate the performance of nonparametric methods and then compare them with classical parametric approaches under symmetric and asymmetric dependence structures within the commonly used logistic family. We also explore two different ways to make nonparametric estimators satisfy the necessary dependence function shape constraints, finding a general improvement in estimator performance either (i) by substituting the estimator with its greatest convex minorant, developing a computational tool to implement this method for dimensions \(D\ge 2\) or (ii) by projecting the estimator onto a subspace of dependence functions satisfying such constraints and taking advantage of Bernstein–Bézier polynomials. Implementing the convex minorant method leads to better estimator performance as the dimensionality increases.

Keywords

Asymmetric logistic model Componentwise maxima Convexity Copula Greatest convex minorant Nonparametric and parametric estimators Pickands dependence function 

Supplementary material

11222_2017_9745_MOESM1_ESM.pdf (40 kb)
Supplementary material 1 (pdf 39 KB)
11222_2017_9745_MOESM2_ESM.zip (5 kb)
Supplementary material 2 (zip 4 KB)

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Sabrina Vettori
    • 1
  • Raphaël Huser
    • 1
  • Marc G. Genton
    • 1
  1. 1.CEMSE DivisionKing Abdullah University of Science and TechnologyThuwalSaudi Arabia

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