A Novel Bayesian Approach for Quantile Regression in High-Dimensional Models

• Activity Number: 318 - Robust Regression Methods: From Independent Observations to Spatial Dependence
• Type: Topic Contributed
• Date/Time: Tuesday, August 9, 2022 : 2:00 PM to 3:50 PM
• Sponsor: International Indian Statistical Association
• Author(s): Min Wang* and Shen Zhang and Mai Dao
• Companies: The University of Texas at San Antonio and The University of Texas at San Antonio and Wichita State University
• Keywords: Asymmetric Laplace distribution; Bayesian regularization; high-dimensional data; Markov Chain Monte Carlo; quantile regression

Abstract

Tian and Song (2020) recently considered a fully Bayesian formulation of the bridge-randomized penalized quantile regression models, which is based on employing the asymmetric Laplace distribution as an auxiliary error distribution and the generalized Gaussian distribution priors for the regression coefficients. However, there exist major drawbacks in performing posterior sampling associated with this formulation in ‘large-p-small-n’ settings, thus limiting its applicability for the analysis of high dimensional data. In this talk, we develop a new Bayesian bridge-randomized quantile regression by making some major adjustments to Tian and Song (2020)’s formulation to overcome the above mentioned drawbacks. Monte Carlo simulation studies indicate that the proposed Bayesian formulation compares favorably with several existing procedures in terms of parameter estimation, variable selection, and prediction across a wide range of scenarios. Finally, a real-data application is provided for illustrating the efficacy of the proposed Bayesian approach.