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Flexible Bayesian Quantile Regression on New Class of Error Distribution | ||
| AL-Qadisiyah Journal For Administrative and Economic sciences | ||
| Volume 28, Issue 1, April 2026, Pages 161-170 PDF (708.04 K) | ||
| Document Type: Research Paper | ||
| DOI: 10.33916/qjae.2026.01161170 | ||
| Authors | ||
| Afraa A. Hamada; Ahmad Naeem Flaih | ||
| University of Al-Qadisiyah | ||
| Abstract | ||
| Quantile regression provides a flexible framework for modeling heterogeneous covariate effects across the conditional distribution of a response variable, yet existing Bayesian quantile regression methods often suffer from inefficiency in estimation accuracy and variable selection, particularly under non-Gaussian errors and high-dimensional settings. In this paper, we propose two new Bayesian quantile regression approaches: a Bayesian quantile regression model with a g-prior (NBQRg) and a Bayesian Lasso quantile regression model (NBLQR) based on the epsilon asymmetric Laplace distribution (EALD) as error term for quantile regression model. The proposed methods are evaluated through extensive simulation studies under a variety of scenarios, including sparse, very sparse, and dense coefficient structures, as well as settings with strong predictor correlations. Data are generated under normal, heavy-tailed, and skewed error distributions, and performance is assessed using the median of mean squared error (MMSE) alongside false positive and false negative rates for variable selection. The simulation results demonstrate that NBQRg consistently achieves lower MMSE than classical quantile regression and existing Bayesian counterparts across all quantiles and error distributions considered. Furthermore, NBLQR exhibits superior variable selection performance, yielding lower false negative rates and competitive false positive rates, particularly in sparse and highly correlated designs. Convergence diagnostics confirm stable posterior inference and efficient mixing of the proposed MCMC algorithms. Overall, the proposed Bayesian quantile regression methods offer substantial improvements in estimation accuracy, robustness, and variable selection, making them well suited for complex and high-dimensional regression problems. Based on the results obtained through simulation applied to real data, the proposed method using the EALD error distribution yields better results compared to the classical method and the BQR method. Furthermore, comparison with the LASSO procedure proved its efficiency in estimating the parameters of the proposed model. Additionally, the Zellner's g-prior model was adopted, as it reduces the variance of the parameter estimates for the proposed regression model, thus enhancing the model's accuracy and increasing its explanatory power. | ||
| Keywords | ||
| Epsilon asymmetric Laplace distribution; Quantile regression; Bayesian estimation; Zellner's g-prior; Simulation | ||
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