Identifying Multivariate Extremes on the Basis of Depth Functions
Fateh Chebana, Taha B.M.J. Ouarda
Centre Eau Terre Environement, Institut National de la Recherche Scientifique, Québec, Canada

Extreme value theory (EVT) is commonly applied in several fields, such as finance, hydrology and environmental modeling. In the univariate context, this theory is extensively developed and it is also widely applied. A number of studies have focused on the extension of EVT to the multivariate setting to be more representative of the studied phenomena. However, most of these studies are based on a direct and technically extension of univariate extremes. In the present work, we are interested in developing a procedure to identify the extremes in a multivariate sample. The present procedure is based on the statistical notion of depth function combined with the orientation of the observations. The extreme identification itself is important and it can also serve as basis for the modeling and the asymptotic studies. The proposed procedure is also employed to detect multivariate peaks-over-thresholds. This method is general and includes several special cases. Furthermore, it is flexible and can be applied to several situations depending on the degree of extreme event risk. The procedure is mainly motivated by application and practical considerations. A simulation study is carried out to evaluate the performance of the procedure. An application, based on air quality data, is presented to show the various elements of the procedure. The procedure is also shown to be useful in other statistical areas.

Keywords: Multivariate extremes; Depth function; Air pollution

Biography: Fateh Chebana is a professor at INRS. He has a PhD from University Paris 6 in statistics. His research interest are modeling and estimation of environmental and hydrological phenomena especially in the multivariate context. His publications are mainly on the developpemt of statistical methods adapted to hydrological and environmental problematiques.