Statistics and Its Interface

Volume 13 (2020)

Number 3

Fully Bayesian $L_{1/2}$-penalized linear quantile regression analysis with autoregressive errors

Pages: 271 – 286



Yuzhu Tian (School of Mathematics and Statistics, Northwest Normal University, Lanzhou, China)

Xinyuan Song (Department of Statistics, Chinese University of Hong Kong, Shatin, N.T., Hong Kong)


In the quantile regression framework, we incorporate Bayesian $L_{1/2}$ and adaptive $L_{1/2}$ penalties into quantile linear regression models with autoregressive (AR) errors to conduct statistical inference. A Bayesian joint hierarchical model is established using the working likelihood of the asymmetric Laplace distribution (ALD). On the basis of the mixture representations of ALD and the generalized Gaussian distribution priors of regression coefficients and AR parameters, a Markov chain Monte Carlo algorithm is developed to conduct posterior inference. Finally, the proposed Bayesian estimation procedures are demonstrated by simulation studies and applied to a real data application concerning the electricity consumption of residential customers.


Autoregressive error, Bayesian quantile regression, generalized Gaussian distribution, Gibbs sampler, $L_{1/2}$ penalty

2010 Mathematics Subject Classification

62F15, 62J07

Received 12 September 2019

Accepted 25 December 2019

Published 22 April 2020