A novel Bayesian computational approach for bridge-randomized quantile regression in high dimensional models

Abstract

A bridge-randomized penalization that employs a prior for the shrinkage parameter, as opposed to the conventional bridge penalization with a fixed penalty, often delivers more superior performance compared to many other traditional shrinkage methods. In this paper, we develop an efficient Bayesian computational algorithm via the two-block Markov Chain Monte Carlo method for the bridge-randomized penalization in quantile regression to perform inference in the high-dimensional ‘large-p’ and ‘large-p-small-n’ settings. To construct a fully Bayesian formulation, we utilize the asymmetric Laplace distribution as an auxiliary error distribution and the generalized Gaussian distribution prior for the regression coefficients. Simulation studies encompassing a wide range of scenarios indicate that the proposed method performs at least as well as, and often better than, other existing procedures in terms of both parameter estimation and variable selection. Finally, a real-data application is provided for illustrative purposes.

KEYWORDS:

• Asymmetric laplace distribution
• Bayesian regularization
• high-dimensional data
• Markov chain Monte Carlo
• quantile regression

Acknowledgments

The authors would like to acknowledge the assistance of the Editor, Dr. Andrei Volodin, as well as the valuable comments and suggestions provided by the Associate Editor and one reviewer. These contributions have significantly enhanced the quality of the manuscript. This work received computational support from the High Performance Computing (HPC) cluster, operated by University Tech Solutions at the University of Texas at San Antonio (UTSA). Additionally, the work of Dr. Min Wang was partially supported by the Internal Research Awards (INTRA) programme from the Vice President for Research, Economic Development, and Knowledge Enterprise at UTSA.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work of Dr. Zifei Han was partially supported by the National Natural Science Foundation of China [grant numbers 12201112 and 12371264], and by the Fundamental Research Funds for the Central Universities, China in UIBE [grant number CXTD14-05].