4,956 research outputs found
Local bilinear multiple-output quantile/depth regression
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.Comment: Published at http://dx.doi.org/10.3150/14-BEJ610 in the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Efficient semiparametric estimation of a partially linear quantile regression model
This paper is concerned with estimating a conditional quantile function that is assumed to be partially linear. The paper develops a simple estimator of the parametric component of the conditional quantile. The semiparametric efficiency bound for the parametric component is derived, and two types of efficient estimators are considered. Asymptotic properties of the proposed estimators are established under regularity conditions. Some Monte Carlo experiments indicate that the proposed estimators perform well in small samples
Backfitting and smooth backfitting for additive quantile models
In this paper, we study the ordinary backfitting and smooth backfitting as
methods of fitting additive quantile models. We show that these backfitting
quantile estimators are asymptotically equivalent to the corresponding
backfitting estimators of the additive components in a specially-designed
additive mean regression model. This implies that the theoretical properties of
the backfitting quantile estimators are not unlike those of backfitting mean
regression estimators. We also assess the finite sample properties of the two
backfitting quantile estimators.Comment: Published in at http://dx.doi.org/10.1214/10-AOS808 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org). With Correction
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