## Bayesian Analysis

### Bayesian regularized quantile regression

Qing Li, Nan Lin, and Ruibin Xi

#### Abstract

Regularization, e.g. lasso, has been shown to be effective in quantile regression in improving the prediction accuracy (Li and Zhu, 2008; Wu and Liu, 2009). This paper studies regularization in quantile regressions from a Bayesian perspective. By proposing a hierarchical model framework, we give a generic treatment to a set of regularization approaches, including lasso, group lasso and elastic net penalties. Gibbs samplers are derived for all cases. This is the first work to discuss regularized quantile regression with the group lasso penalty and the elastic net penalty. Both simulated and real data examples show that Bayesian regularized quantile regression methods often outperform quantile regression without regularization and their non-Bayesian counterparts with regularization.

#### Article information

Source
Bayesian Anal. Volume 5, Number 3 (2010), 533-556.

Dates
First available in Project Euclid: 22 June 2012

https://projecteuclid.org/euclid.ba/1340380540

Digital Object Identifier
doi:10.1214/10-BA521

Mathematical Reviews number (MathSciNet)
MR2719666

Zentralblatt MATH identifier
1330.62143

#### Citation

Li, Qing; Xi, Ruibin; Lin, Nan. Bayesian regularized quantile regression. Bayesian Anal. 5 (2010), no. 3, 533--556. doi:10.1214/10-BA521. https://projecteuclid.org/euclid.ba/1340380540

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