Department of Applied Statistics
Johannes Kepler University Linz, Austria
Departmento de Matematica
Universidad Tecnica Federico Santa Maria, Valparaiso, Chile
On favorable extremes modeling with applications
We will concentrate on several methodological issues of parametric models for Extreme Values. Hill (1975) derived a procedure of Pareto tail estimation by the MLE. Later on, many authors tried to robustify the Hill estimator, but they still rely on maximum likelihood, e.g. Alves (2001) introduced a new lower bound. However, the influence function of the Hill estimator is slowly increasing, but unbounded. Hill's procedure is thus not robust and many authors tried to make the original Hill robust. In Fabian (2001) a new method of score moment estimators has been proposed. It appeared that these score moment estimators are robust for a heavy tailed distributions. We will compare t-estimation with other favorable heavy-tails estimation introduced in Brazauskas and Serfling (2001). For the case of Pareto distribution, the t-Hill estimator procedure based on the score moment estimator has been investigated by Stehlik et al. (2102) for optimal testing for normality against Pareto tail. We will illustrate that t-Hill estimator is a "naturally" robust, distribution sensitive heavy tail estimator and prove its weak consistency together with its good small sample properties and some further structural properties. Theoretical aspects of the talks will be highlighted on two applications, namely modelling of methane flux and snow extremes modelling.
Sponsored by the Department of Mathematical Sciences
Host: Yulia Gel
Refreshments will be served in Room TBD 30 minutes before the talk begins.