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A0158
Title: The role of generalized means in multivariate extreme value statistics Authors:  Ivette Gomes - FCiencias.ID, Universidade de Lisboa and CEAUL (Portugal) [presenting]
Abstract: Modern risk assessment of the amount of tail dependence is nowadays crucial in the most diverse fields, like finance and insurance, among others, and the correlation structure is usually not enough to describe such a tail dependence. Given a pair $(X,Y)$, with margins, $(F_X, F_Y)$, the \textit{tail dependence coefficient} (TDC), denoted by $\eta$, can be defined as a limiting conditional probability, $\eta:=\lim_{t\rightarrow\infty} P\left(F_X(X)>1-1/t| F_Y(Y)>1-1/t \right)$. The standardization of the margins to unit Fr\'{e}chet margins, enables the estimation of the TDC in a way similar to the estimation of the {\it extreme value index} (EVI) associated with $Z:=\min (X,Y)$. Indeed, $P(Z>z)=P(X>z, Y>z)=z^{-1/\eta}{\cal L}(z)$, where ${\cal L}(\cdot)$ is a slowly-varying function at infinity. \textit{Generalized means} (GMs) have recently been successfully used for the estimation of parameters of extreme events, like the EVI and the value at risk. Now, GMs are used under a multivariate framework, essentially for the estimation of the TDC, in bivariate extreme value statistics. Associated asymptotically unbiased estimators are also constructed. The finite-sample behavior as well as robustness, regarding sensitivity to the extreme value dependence assumption, is assessed through small-scale Monte-Carlo simulation studies.