Local bilinear multiple-output quantile/depth regression
Abstract
A new quantile regression concept, based on a directional version of Koenker and Bassett's traditional single-output one, has been introduced in [Ann. Statist. (2010) 38 635-669] 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.
Cite
@article{arxiv.1507.07754,
title = {Local bilinear multiple-output quantile/depth regression},
author = {Marc Hallin and Zudi Lu and Davy Paindaveine and Miroslav Šiman},
journal= {arXiv preprint arXiv:1507.07754},
year = {2015}
}
Comments
Published at http://dx.doi.org/10.3150/14-BEJ610 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)