Composite quantile regression and the oracle Model Selection Theory

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dc.creatorZou, Hui
dc.creatorYuan, Ming
dc.date2008-06-18
dc.date.accessioned2026-07-07T12:19:35Z
dc.date.available2026-07-07T12:19:35Z
dc.descriptionCoefficient estimation and variable selection in multiple linear regression is routinely done in the (penalized) least squares (LS) framework. The concept of model selection oracle introduced by Fan and Li [J. Amer. Statist. Assoc. 96 (2001) 1348--1360] characterizes the optimal behavior of a model selection procedure. However, the least-squares oracle theory breaks down if the error variance is infinite. In the current paper we propose a new regression method called composite quantile regression (CQR). We show that the oracle model selection theory using the CQR oracle works beautifully even when the error variance is infinite. We develop a new oracular procedure to achieve the optimal properties of the CQR oracle. When the error variance is finite, CQR still enjoys great advantages in terms of estimation efficiency. We show that the relative efficiency of CQR compared to the least squares is greater than 70% regardless the error distribution. Moreover, CQR could be much more efficient and sometimes arbitrarily more efficient than the least squares. The same conclusions hold when comparing a CQR-oracular estimator with a LS-oracular estimator.
dc.descriptionPublished in at http://dx.doi.org/10.1214/07-AOS507 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/0806.2905
dc.identifierhttp://arxiv.org/abs/0806.2905
dc.identifierAnnals of Statistics 2008, Vol. 36, No. 3, 1108-1126
dc.identifierdoi:10.1214/07-AOS507
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/212805
dc.subjectStatistics Theory
dc.subject62J05 (Primary) 62J07 (Secondary)
dc.titleComposite quantile regression and the oracle Model Selection Theory
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