Multiple-Output Functional Quantile Regression

• Activity Number: 283
• Type: Invited
• Date/Time: Tuesday, August 11, 2015 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Davy Paindaveine* and Germain Van Bever
• Companies: Université libre de Bruxelles and The Open University
• Keywords: Functional regression ; Quantile regression ; Conditional Depth

Abstract

We consider a multiple-output functional regression problem where the response is a random d-vector Y and the covariate X(t) is of a functional nature. In that framework, we define a concept of directional regression quantile, which extends the finite-dimensional concept from Hallin, Paindaveine and Siman (2010) and Hallin, Lu, Paindaveine and Siman (2015). This requires considering a (single-output) quantile regression problem that is of a "partially functional" nature, in the sense that it involves both finite-dimensional and functional covariates. We show that, parallel to the finite-dimensional case, conditional depth regions of the response Y can be obtained from the proposed directional regression quantiles. The results are illustrated on simulated and real data sets.