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Local bilinear multiple-output quantile/depth regression
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SYSNO ASEP 0446857 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Local bilinear multiple-output quantile/depth regression Author(s) Hallin, M. (BE)
Lu, Z. (GB)
Paindaveine, D. (BE)
Šiman, Miroslav (UTIA-B) RID, ORCIDSource Title Bernoulli. - : International Statistical Institute - ISSN 1350-7265
Roč. 21, č. 3 (2015), s. 1435-1466Number of pages 32 s. Publication form Print - P Language eng - English Country NL - Netherlands Keywords conditional depth ; growth chart ; halfspace depth ; local bilinear regression ; multivariate quantile ; quantile regression ; regression depth Subject RIV BA - General Mathematics R&D Projects 1M06047 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) Institutional support UTIA-B - RVO:67985556 UT WOS 000356993100007 EID SCOPUS 84938592517 DOI 10.3150/14-BEJ610 Annotation 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. Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2016
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