Local bilinear multiple-output quantile/depth regression

0446857 - ÚTIA 2016 RIV NL eng J - Journal Article
Hallin, M. - Lu, Z. - Paindaveine, D. - Šiman, Miroslav
Local bilinear multiple-output quantile/depth regression.
Bernoulli. Roč. 21, č. 3 (2015), s. 1435-1466. ISSN 1350-7265. E-ISSN 1573-9759
R&D Projects: GA MŠMT(CZ) 1M06047
Institutional support: RVO:67985556
Keywords : conditional depth * growth chart * halfspace depth * local bilinear regression * multivariate quantile * quantile regression * regression depth
Subject RIV: BA - General Mathematics
Impact factor: 1.372, year: 2015
http://library.utia.cas.cz/separaty/2015/SI/siman-0446857.pdf

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.
Permanent Link: http://hdl.handle.net/11104/0248946