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Anna Kiriliouk, UNamur Print
Thursday, 20 December 2018, 12:15 - 13:15

Anna Kiriliouk, UNamur

Peaks over thresholds modeling with multivariate generalized Pareto distributions.

Abstract: Modeling univariate extreme events such as floods and stock crashes is often done using the peaks over thresholds method, that is, by fitting a generalized Pareto distribution to all observations that exceed some high threshold. However, many applications in extreme value theory are inherently multivariate, and one is interested in characterizing the degree of tail dependence between the components of a multivariate vector. The multivariate generalized Pareto distribution arises as the limit of a suitably normalized vector conditioned upon at least one component of that vector being extreme. We discuss a construction device which allows us to develop new parametric tail dependence models. A censored likelihood estimation procedure is proposed together with a threshold selection procedure and several goodness-of-fit diagnostics. These methods are illustrated in an application aimed at calculating the Fraction of Attributable Risk, a measure often used by climate scientists to quantify the human impact on climate change. 

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