• Citer

Local constant and local bilinear multiple-output quantile regression

par Hallin, Marc ;Lu, Zudi;Paindaveine, Davy ;Siman, Miroslav
Référence Bernoulli, 21, page (1435-1466)
Publication Publié, 2015

Article révisé par les pairs

• Accès en ligne
• Détails
• Contenu
• Statistiques

Résumé :

A new quantile regression concept, based on a directional version of Koenker and Bassett's traditional single-output one, has been introduced in [Hallin, Paindaveine and Siman, Annals of Statistics 2010, 635-703] for multiple-output location/linear regression 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.