0446857 20240103210501.520150904235959.9 000356993100007 84938592517 10.3150/14-BEJ610 32 s. P cav_un_epca*02522181350-7265213 (2015)1435-1466International Statistical Institute conditional depth growth chart halfspace depth local bilinear regression multivariate quantile quantile regression regression depth cav_un_auth*0280802 Hallin M. BE cav_un_auth*0319159 Lu Z. GB 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/2015/SI/siman-0446857.pdf 1M06047 GA MŠk CZ cav_un_auth*0217941 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. 2016 BA 4 A hod 4ah 20231122141116.4 RVO:67985556 http://hdl.handle.net/11104/0248946 cav_un_auth*0319160 Universite libre de Bruxelles BE cav_un_auth*0309080 Princeton University US cav_un_auth*0319161 University of Southampton GB 1 Department of Stochastic Informatics UTIA-B 10103 STATISTICS & PROBABILITY S STATISTICS&PROBABILITY 1.359 0.231 9.4 0.00955 1.692 1565 2.115 Q1 1.309 91 Q2 81.674 70.3 Q1 Q1 70.325 2015 Soubory v repozitáři: siman-0446857.pdf 84938592517 SCOPUS 000356993100007 WOS cav_un_epca*0252218 Bernoulli 1350-7265 1573-9759 Roč. 21 č. 3 2015 1435 1466 International Statistical Institute