Local Multiple-Output Quantile Regression

A new quantile regression concept, based on a directional version of Koenker and Bassett's traditional single-output one, has recently been introduced by Hallin, Paindaveine, and Siman (2010) for multiple-output problems. The polyhedral contours provided by the empirical counterpart of that concept, however, cannot adapt to unknown nonlinear and/or heteroskedastic dependencies. This paper therefore introduces local constant and local linear (actually, bilinear) versions of those contours, which both allow to asymptotically recover the conditional halfspace depth contours that completely characterize the response's conditional distributions. Bahadur representation and asymptotic normality results are established. Illustrations are provided both on simulated and real data.

(Joint work with Marc Hallin, Zudi Lu, and Miroslav Siman)