B0249
Title: Estimation of marginal excess moments for Weibull-type distributions
Authors: Armelle Guillou - Strasbourg university (France) [presenting]
Abstract: The estimation of the marginal excess moment is considered, which is defined for a random vector $(X, Y)$ and a parameter $\beta>0$ as $E[(X-Q_X(1-p))_+^\beta| Y>Q_Y(1-p)]$ provided $E|X|^\beta < \infty$, and where $Q_X$ and $Q_Y$ are the quantile functions of $X$ and $Y$ respectively, and $p\in(0, 1)$. The interest is in the situation where the random variable $X$ is of Weibull-type while the distribution of $Y$ is kept general, the extreme dependence structure of $(X, Y)$ converges to that of bivariate extreme value distribution, and $p \to 0$ as the sample size $n \to \infty$. By using extreme value arguments an estimator is introduced for the marginal excess moment and its limiting distribution is derived. The finite sample properties of the proposed estimator are evaluated with a simulation study and the practical applicability is illustrated on a dataset of wave heights and wind speeds.
