Open Access
November 2019 Adaptively weighted group Lasso for semiparametric quantile regression models
Toshio Honda, Ching-Kang Ing, Wei-Ying Wu
Bernoulli 25(4B): 3311-3338 (November 2019). DOI: 10.3150/18-BEJ1091


We propose an adaptively weighted group Lasso procedure for simultaneous variable selection and structure identification for varying coefficient quantile regression models and additive quantile regression models with ultra-high dimensional covariates. Under a strong sparsity condition, we establish selection consistency of the proposed Lasso procedure when the weights therein satisfy a set of general conditions. This consistency result, however, is reliant on a suitable choice of the tuning parameter for the Lasso penalty, which can be hard to make in practice. To alleviate this difficulty, we suggest a BIC-type criterion, which we call high-dimensional information criterion (HDIC), and show that the proposed Lasso procedure with the tuning parameter determined by HDIC still achieves selection consistency. Our simulation studies support strongly our theoretical findings.


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Toshio Honda. Ching-Kang Ing. Wei-Ying Wu. "Adaptively weighted group Lasso for semiparametric quantile regression models." Bernoulli 25 (4B) 3311 - 3338, November 2019.


Received: 1 April 2017; Revised: 1 May 2018; Published: November 2019
First available in Project Euclid: 25 September 2019

zbMATH: 07110139
MathSciNet: MR4010956
Digital Object Identifier: 10.3150/18-BEJ1091

Keywords: Additive models , B-spline , high-dimensional information criteria , Lasso , structure identification , varying coefficient models

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability

Vol.25 • No. 4B • November 2019
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