Robust Variable Selection via Bayesian LASSO-Composite Quantile Regression with Empirical Likelihood: A Hybrid Sampling Approach

Ruisi Nan, Jingwei Wang, Hanfang Li and Youxi Luo ()
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Ruisi Nan: School of Science, Hubei University of Technology, Wuhan 430068, China
Jingwei Wang: School of Science, Hubei University of Technology, Wuhan 430068, China
Hanfang Li: School of Science, Hubei University of Technology, Wuhan 430068, China
Youxi Luo: School of Science, Hubei University of Technology, Wuhan 430068, China

Mathematics, 2025, vol. 13, issue 14, 1-20

Abstract: Since the advent of composite quantile regression (CQR), its inherent robustness has established it as a pivotal methodology for high-dimensional data analysis. High-dimensional outlier contamination refers to data scenarios where the number of observed dimensions ( p ) is much greater than the sample size ( n ) and there are extreme outliers in the response variables or covariates (e.g., p / n > 0.1). Traditional penalized regression techniques, however, exhibit notable vulnerability to data outliers during high-dimensional variable selection, often leading to biased parameter estimates and compromised resilience. To address this critical limitation, we propose a novel empirical likelihood (EL)-based variable selection framework that integrates a Bayesian LASSO penalty within the composite quantile regression framework. By constructing a hybrid sampling mechanism that incorporates the Expectation–Maximization (EM) algorithm and Metropolis–Hastings (M-H) algorithm within the Gibbs sampling scheme, this approach effectively tackles variable selection in high-dimensional settings with outlier contamination. This innovative design enables simultaneous optimization of regression coefficients and penalty parameters, circumventing the need for ad hoc selection of optimal penalty parameters—a long-standing challenge in conventional LASSO estimation. Moreover, the proposed method imposes no restrictive assumptions on the distribution of random errors in the model. Through Monte Carlo simulations under outlier interference and empirical analysis of two U.S. house price datasets, we demonstrate that the new approach significantly enhances variable selection accuracy, reduces estimation bias for key regression coefficients, and exhibits robust resistance to data outlier contamination.

Keywords: composite quantile regression; empirical likelihood; Bayesian LASSO penalty; hybrid Gibbs sampling algorithm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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