NDLI: Bayesian regularized regression based on composite quantile method

Content Provider	SpringerLink
Author	Liu, Ji cai Lü, Ya zhao Zhang, Ri quan Zhao, Wei hua
Copyright Year	2016
Abstract	Recently, variable selection based on penalized regression methods has received a great deal of attention, mostly through frequentist’s models. This paper investigates regularization regression from Bayesian perspective. Our new method extends the Bayesian Lasso regression (Park and Casella, 2008) through replacing the least square loss and Lasso penalty by composite quantile loss function and adaptive Lasso penalty, which allows different penalization parameters for different regression coefficients. Based on the Bayesian hierarchical model framework, an efficient Gibbs sampler is derived to simulate the parameters from posterior distributions. Furthermore, we study the Bayesian composite quantile regression with adaptive group Lasso penalty. The distinguishing characteristic of the newly proposed method is completely data adaptive without requiring prior knowledge of the error distribution. Extensive simulations and two real data examples are used to examine the good performance of the proposed method. All results confirm that our novel method has both robustness and high efficiency and often outperforms other approaches.
Ending Page	512
Page Count	18
Starting Page	495
File Format	PDF
ISSN	01689673
e-ISSN	16183932
Journal	Acta Mathematicae Applicatae Sinica
Issue Number	2
Volume Number	32
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2016-04-29
Publisher Place	Berlin, Heidelberg
Access Restriction	Subscribed
Subject Keyword	Hypothesis testing Gibbs sampler Lasso adaptive Lasso Theoretical, Mathematical and Computational Physics Nonparametric regression composite quantile regression variable selection Applications of Mathematics Math Applications in Computer Science
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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