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August 2015 Local bilinear multiple-output quantile/depth regression
Marc Hallin, Zudi Lu, Davy Paindaveine, Miroslav Šiman
Bernoulli 21(3): 1435-1466 (August 2015). DOI: 10.3150/14-BEJ610


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.


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Marc Hallin. Zudi Lu. Davy Paindaveine. Miroslav Šiman. "Local bilinear multiple-output quantile/depth regression." Bernoulli 21 (3) 1435 - 1466, August 2015.


Received: 1 August 2012; Revised: 1 May 2013; Published: August 2015
First available in Project Euclid: 27 May 2015

zbMATH: 06470446
MathSciNet: MR3352050
Digital Object Identifier: 10.3150/14-BEJ610

Rights: Copyright © 2015 Bernoulli Society for Mathematical Statistics and Probability


Vol.21 • No. 3 • August 2015
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