Event
Klaus Herrmann, Department of Mathematics and Statistics, Concordia University
Thursday, April 20, 2017 15:30to16:30
Seminar Statistique Sherbrooke, 2500 Boul de L'Universit茅, Sherbrooke, QC, CA
Multivariate Geometric Expectiles.
In this talk we introduce a generalization of expectiles for d-dimensional multivariate distribution functions. This generalization is based on geometric quantiles introduced in Chaudhuri (1996). The resulting geometric expectiles are unique solutions to a convex risk minimization problem and are given by $d$-dimensional vectors. We discuss their behaviour under common data transformations such as translations, scaling and rotations of the underlying data. Geometric expectiles also obey symmetry properties comparable to the univariate case. We furthermore discuss elicitability in the context of geometric expectiles and multivariate risk measures in general. We show that a consistent estimator is readily available by the sample version. Finally, we exemplify the usage of geometric expectiles as risk measures in a number of multivariate settings, highlighting the influence of varying margins and dependence structures. Joint work with Marius Hofert and M茅lina Mailhot