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https://doi.org/10.1214/13-BA817

has been cited by the following article:

• TITLE: Bayesian Regularized Quantile Regression Analysis Based on Asymmetric Laplace Distribution

  AUTHORS: Qiaoqiao Tang, Haomin Zhang, Shifeng Gong

  KEYWORDS: Asymmetric Laplace Distribution, Gibbs Sampling, Adaptive Lasso, Lasso, Bayesian Regularization Quantile Regression

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.8 No.1, January 6, 2020

  ABSTRACT: In recent years, variable selection based on penalty likelihood methods has aroused great concern. Based on the Gibbs sampling algorithm of asymmetric Laplace distribution, this paper considers the quantile regression with adaptive Lasso and Lasso penalty from a Bayesian point of view. Under the non-Bayesian and Bayesian framework, several regularization quantile regression methods are systematically compared for error terms with different distributions and heteroscedasticity. Under the error term of asymmetric Laplace distribution, statistical simulation results show that the Bayesian regularized quantile regression is superior to other distributions in all quantiles. And based on the asymmetric Laplace distribution, the Bayesian regularized quantile regression approach performs better than the non-Bayesian approach in parameter estimation and prediction. Through real data analyses, we also confirm the above conclusions.