Statistical Papers

, Volume 60, Issue 1, pp 173–197 | Cite as

Adaptive group LASSO selection in quantile models

  • Gabriela CiupercaEmail author
Regular Article


The paper considers a linear model with grouped explanatory variables. If the model errors are not with zero mean and bounded variance or if model contains outliers, then the least squares framework is not appropriate. Thus, the quantile regression is an interesting alternative. In order to automatically select the relevant variable groups, we propose and study here the adaptive group LASSO quantile estimator. We establish the sparsity and asymptotic normality of the proposed estimator in two cases: fixed number and divergent number of variable groups. Numerical study by Monte Carlo simulations confirms the theoretical results and illustrates the performance of the proposed estimator.


Group selection Quantile model Adaptive LASSO Selection consistency Oracle properties 

Mathematics Subject Classification

62J05 62J07 



The author sincerely thanks the Editor and two anonymous referees for their valuable comments which improved the quality of the paper.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.CNRS, UMR 5208, Institut Camille Jordan, Bat. BraconnierUniversité Lyon 1, Université de LyonVilleurbanne CedexFrance

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