|When the POT–approach fails: super heavy tailed
distributions and covariate information
Ulf Cormann (speaker) and R.D. Reiss, University of Siegen, Germany.
Wednesday, March 4, 2009
3:00 pm, 223 Weber
We consider the case that the conditional distribution of a ran-
dom variable Y given X = x is in the domain of attraction of a generalized
Pareto distribution (GPD), which parameters depend on x. In many cases
this entails that the distribution of Y is not in the domain of attraction of
any GPD anymore. We distinguish two cases whether the covariate variable
X can be observed or not.
Considering the first case we propose a conditional point process model
to estimate the tail of the conditional distribution via Maximum–Likelihood.
In the second case we derive limiting distribution of exceedances from super–
heavy tailed distributions using non–linear transformations.
Finally some open questions are addressed concerning threshold selection
in the first case and discriminating between heavy and super–heavy tailed
distributions in the second case.