Probabilities of Extreme Half-Spaces and Other Marginal Parameters of Multivariate Distributions
Stephan Morgenthaler
Mathematics, EPFL (Ecole Polytechnique Fédérale de Lausanne), Lausanne, Switzerland

In this talk we will present a method based on the generalized Pareto distribution for estimating probabilities of extremal half-spaces involving multivariate observations. If the multivariate distribution is elliptical we can use affine transformations between half-spaces in order to combine estimators based on several one-dimensional projections of the multivariate data set, rather than using a single projection. More reliable estimators result from this practice. Furthermore, the technique suggests some natural estimates of the sampling variance. This same idea can be used to estimate any marginal parameter of a multivariate distribution. If time permits, an application to risk assessment in financial data will be given.

Keywords: multivariate data; marginal parameters; Pareto distribution

Biography: Stephan Morgenthaler studied mathematics at ETH in Zurich (Switzerland) and did his Ph.D. in Statistics at Princeton University. His academic career has taken him from an instructorship at M.I.T., to an assistant professorship at Yale University and a position at EPF in Lausanne (the Ecole polytechnique fédérale de Lausanne). His main interests are data analysis, robustness and medical and genetic statistics.