0364128 20250213151359.420110920235959.9 000284983600001 78649445678 10.1016/j.jmva.2010.08.004 20 s. cav_un_epca*02570440047-259X1022 (2011)193-212Elsevier multivariate quantile quantile regression multiple-output regression halfspace depth portfolio optimization value-at risk cav_un_auth*0274302 Paindaveine D. BE cav_un_auth*0266474 Šiman Miroslav Stochastická informatika Department of Stochastic Informatics SI SI UTIA-B Department of Stochastic Informatics Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2011/SI/siman-0364128.pdf 1M06047 GA MŠk CZ cav_un_auth*0217941 Fonds National de la Recherche Scientifique Commision EC BE CEZ:AV0Z10750506 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. 2012 BA 2 4 A 4a 20231122134646.5 http://hdl.handle.net/11104/0199690 STATISTICSPROBABILITY 1.088 0.193 8 0.01376 1.032 2282 109 1.677 Q1 63.142 51.293 Q2 Q1 2011 Soubory v repozitáři: siman-0364128.pdf 78649445678 SCOPUS 000284983600001 WOS cav_un_epca*0257044 Journal of Multivariate Analysis 0047-259X 1095-7243 Roč. 102 č. 2 2011 193 212 Elsevier