Title: Semi-parametric estimation of the tail dependence coefficient through generalized means
Authors: Ivette Gomes - FCiencias.ID, Universidade de Lisboa and CEAUL (Portugal) [presenting]
Abstract: Many examples in the most diverse fields of application show the need for statistical methods of analysis of extremes of multivariate data. And a crucial issue that appears when there is more than one variable is that of dependence. The study of multivariate extremes can be split essentially in two parts: the marginal distributions and the dependence structure. In first place, the margins are dealt with, and univariate extreme value theory techniques are used. In second place, we have to deal with dependence, also often dependent on univariate techniques, just as will be seen for the estimation of the tail dependence coefficient (TDC). Indeed, and thinking on a bivariate framework, $(X,Y)$, after the standardization of the margins to a unit Fr\'echet distribution, the TDC appears as the reciprocal of the regularly varying exponent of a Pareto-type right-tail function of the differences between the margins. Different generalized means have been recently used in a successful estimation of the extreme value index, among other parameters of univariate extreme events, and will be now used for the TDC-estimation.