On directional multiple-output quantile regression

0364128 - ÚTIA 2012 RIV US eng J - Journal Article
Paindaveine, D. - Šiman, Miroslav
On directional multiple-output quantile regression.
Journal of Multivariate Analysis. Roč. 102, č. 2 (2011), s. 193-212. ISSN 0047-259X
R&D Projects: GA MŠMT(CZ) 1M06047
Grant - others:Commision EC(BE) Fonds National de la Recherche Scientifique
Institutional research plan: CEZ:AV0Z10750506
Keywords : multivariate quantile * quantile regression * multiple-output regression * halfspace depth * portfolio optimization * value-at risk
Subject RIV: BA - General Mathematics
Impact factor: 0.879, year: 2011
http://library.utia.cas.cz/separaty/2011/SI/siman-0364128.pdf

This paper sheds some new light on projection quantiles. It studies the subgradient conditions associated with these quantiles in a general regression context, introduces Lagrange multipliers with rich interpretation, provides another proof that corresponding projection quantile regions coincide with the halfspace depth ones, and shows how this equivalence could be used for exact computation of the latter regions by means of projection quantiles. Furthermore, it demonstrates that the regression quantile regions introduced in Hallin, Paindaveine and Siman (2010) can also be obtained from projection (regression) quantiles, which may lead to a faster computation of those regions in some particular cases.
Permanent Link: http://hdl.handle.net/11104/0199690