Quantile regression shrinkage and selection via the Lqsso

被引:3
作者
Daneshvar, Alireza [1 ]
Golalizadeh, Mousa [1 ]
机构
[1] Tarbiat Modares Univ, Dept Stat, Tehran, Iran
关键词
Quantile regression; shrinkage; oracle property; consistency; lasso; VARIABLE SELECTION; ADAPTIVE LASSO; ASYMPTOTICS;
D O I
10.1080/10543406.2023.2198593
中图分类号
R9 [药学];
学科分类号
1007 ;
摘要
Quantile regression has recently received a considerable attention due to its remarkable development in enriching the variety of regression models. Many efforts have been made to blend different penalty and loss function to extend or develop novel regression models that are unique from different perspectives. Bearing in mind that the lasso quantile regression model ignores the randomness of the realizations in the penalty part, we propose a new penalty for the quantile regression models. Similar to the adaptive lasso quantile regression model, the proposed model simultaneously does estimation and variable selection tasks. We call the new model 'lqsso-QR', standing for the least quantile shrinkage and selection operator quantile regression. In this article, we present a sufficient and necessary condition for the variable selection of the lasso quantile regression to enjoy the consistent property. We show that the lqsso-QR follows oracle properties under some mild conditions. From computational perspective, we apply an efficient algorithm, originally developed for the lasso quantile regression. Using simulation studies, we elaborate on the superiority of the proposed model compared with other lasso-type penalties, especially regarding relative prediction error. Also, an application of our method to a real-life data; the rat eye data, is reported.
引用
收藏
页码:297 / 322
页数:26
相关论文
共 50 条
[41]   GRADIENT-INDUCED MODEL-FREE VARIABLE SELECTION WITH COMPOSITE QUANTILE REGRESSION [J].
He, Xin ;
Wang, Junhui ;
Lv, Shaogao .
STATISTICA SINICA, 2018, 28 (03) :1521-1538
[42]   Variable selection in additive quantile regression using nonconcave penalty [J].
Zhao, Kaifeng ;
Lian, Heng .
STATISTICS, 2016, 50 (06) :1276-1289
[43]   Variable selection in heteroscedastic single-index quantile regression [J].
Christou, Eliana ;
Akritas, Michael G. .
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2018, 47 (24) :6019-6033
[44]   Regularized Bayesian quantile regression [J].
El Adlouni, Salaheddine ;
Salaou, Garba ;
St-Hilaire, Andre .
COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, 2018, 47 (01) :277-293
[45]   Bayesian Regularized Quantile Regression [J].
Li, Qing ;
Xi, Ruibin ;
Lin, Nan .
BAYESIAN ANALYSIS, 2010, 5 (03) :533-556
[46]   M-quantile regression shrinkage and selection via the Lasso and Elastic Net to assess the effect of meteorology and traffic on air quality [J].
Ranalli, M. Giovanna ;
Salvati, Nicola ;
Petrella, Lea ;
Pantalone, Francesco .
BIOMETRICAL JOURNAL, 2023, 65 (08)
[47]   Optimal portfolio selection using quantile and composite quantile regression models [J].
Aghamohammadi, A. ;
Dadashi, H. ;
Sojoudi, Mahdi ;
Sojoudi, Meysam ;
Tavoosi, M. .
COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, 2024, 53 (07) :3047-3057
[48]   Regression coefficient and autoregressive order shrinkage and selection via the lasso [J].
Wang, Hansheng ;
Li, Guodong ;
Tsai, Chih-Ling .
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY, 2007, 69 :63-78
[49]   SCAD-penalized quantile regression for high-dimensional data analysis and variable selection [J].
Amin, Muhammad ;
Song, Lixin ;
Thorlie, Milton Abdul ;
Wang, Xiaoguang .
STATISTICA NEERLANDICA, 2015, 69 (03) :212-235
[50]   QUANTILE REGRESSION MODELING WITH GROUP LEAST ABSOLUTE SHRINKAGE AND SELECTION OPERATOR CLASSIFICATION ON TUBERCULOSIS DATA [J].
Usman, Irwan ;
Islamiyati, Anna ;
Herdiani, Erna Tri .
COMMUNICATIONS IN MATHEMATICAL BIOLOGY AND NEUROSCIENCE, 2024,