Multivariate nonparametric estimation of the Pickands dependence function using Bernstein polynomials

By Giulia Marcon, Simone A. Padoan, Philippe Naveau, Pietro Muliere, Johan Segers. 2014

63 citations recorded by the source corpus.

Abstract Many applications in risk analysis require the estimation of the dependence among multivariate maxima, especially in environmental sciences. Such dependence can be described by the Pickands dependence function of the underlying extreme-value copula. Here, a nonparametric estimator is constructed as the sample equivalent of a multivariate extension of the madogram. Shape constraints on the family of Pickands dependence functions are taken into account by means of a representation in terms of Bernstein polynomials. The large-sample theory of the estimator is developed and its finite-sample performance is evaluated with a simulation study. The approach is illustrated with a dataset of weekly maxima of hourly rainfall in France recorded from 1993 to 2011 at various weather stations all over the country. The stations are grouped into clusters of seven stations, where our interest is in the extremal dependence within each cluster.

Subfields: Finance, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/c66065f1946dfd45552cd264818a4814823642c3

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Citations in the corpus

Non-Stationary Dependence Structures for Spatial Extremes (2014, methodology): “Empirical estimates are calculated using the projection method of Marcon et al. (2014) based on the non-parametric Pickands dependence estimator of Capéraà et al. (1997).”
Graphical models for extremes (2018, background): “, 2011) and finance (McNeil et al., 2015); see also Embrechts et al. (1997) and Beirlant et al. (2004). In the multivariate setting, d 2, the result of the extrapolation strongly depends on the strength of extremal dependence between the components of X.”