A class of exponential families in the Frechet MDA with an infinite dimensional parameter is considered. The tail index and other parameters are estimated using finite dimensional approximations. Asymptotic properties are discussed under suitable parametric and semiparametric conditions. The resulting class of tail index estimators is compared to optimal nonparametric methods known in the literature. Finite sample behaviour is illustrated by simulations and data examples.
Keywords: tail index; exponential families
Biography: After concluding a Master in Mathematical Finance at the University of Konstanz in 2008, I started my PhD project at the Department of Mathematics and Statistics at the University of Konstanz. The title of my PhD thesis is “On Estimation of Heavy Tails.”