Local constant and local bilinear multiple-output quantile regression
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Date
2012-08-01
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Abstract
A new quantile regression concept, based on a directional version
of Koenker and Bassett’s traditional single-output one, has been
introduced in [Hallin, Paindaveine and ˇSiman, Annals of Statistics
2010, 635-703] for multiple-output regression problems. The polyhedral
contours provided by the empirical counterpart of that concept,
however, cannot adapt to nonlinear and/or heteroskedastic dependencies.
This paper therefore introduces local constant and local linear
versions of those contours, which both allow to asymptotically
recover the conditional halfspace depth contours of the response. In
the multiple-output context considered, the local linear construction
actually is of a bilinear nature. Bahadur representation and asymptotic
normality results are established. Illustrations are provided both
on simulated and real data.