Department Seminars and Colloquia



Local Bilinear Multiple-Output Quantile Regression: from L1 Optimization to Regression Depth

Statistics Seminar

Marc Hallin


Institution: Universite Libre de Bruxelles, Belgium
Date: Tue 6th March 2012
Time: 2:00 PM
Location: Room 213, Richard Berry Building, University of Melbourne

Abstract: A new multiple output concept of quantile regression, based on a directional version of Koenker and Bassett’s traditional one, has been introduced in Hallin, Paindaveine and Siman (Annals of Statistics 2010, 635-703), essentially for multivariate location problems. The empirical counterpart of that concept produces polyhedral contours that (in the location case) coincide with the Tukey halfspace depth contours. In a regression context, however, that concept cannot account for nonlinear or/and heteroscedastic dependencies. A local bilinear version of those contours is proposed here, which asymptotically recovers the conditional halfspace depth contours of the multiple-output response. A Bahadur representation is established, along with asymptotic normality results. Examples are provided.

(Joint work with Zudi Lu, Davy Paindaveine, and Miroslav Siman)

For More Information: contact: Mihee Lee. email: miheel@unimelb.edu.au