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Title: The use of Bernstein polynomials for modelling the extremal dependence Authors:  Simone Padoan - Bocconi University (Italy) [presenting]
Abstract: A simple approach for modelling multivariate extremes is to consider the vector of component-wise maxima and their max-stable distributions. The extremal dependence can be inferred by estimating the angular measure or, alternatively, the Pickands dependence function. A flexible means for modelling such a dependence structure is the use of polynomials in the Bernstein form. For example, in the bivariate case, we describe a simple nonparametric Bayesian model that allows the estimation of both functional representations, satisfying the constraints required in order to provide a valid extremal dependence. This task is attained by placing a prior distribution on the Bernstein polynomials' coefficients, which gives probability one to the set of valid functions. The prior is extended to the polynomial degree, making our approach fully nonparametric. We show how to infer the extremal dependence, represented by Bernstein polynomials, using also the frequentist approach. With both approaches our proposal turns out to be a flexible framework for estimating component-wise maxima as well as the threshould exceedances. We show the utility of our proposed methods by a simulation study and a real data analysis.