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<p>Linear inequality constraints enhance the precision of parameter estimation by constraining parameters to a more confined space. This paper introduces a Bayesian quantile regression model with linear inequality constraints. To rigorously enforce these inequality constraints within the Bayesian framework, we adopt truncated prior distributions. Leveraging asymmetric Laplace distributions, we propose two novel Gibbs sampling methods based on truncated normal and truncated Laplace prior distributions, which involve sampling from truncated normal and generalized inverse Gaussian distributions, respectively. Our approach extends the constraints from solely inequality-based to a comprehensive framework incorporating both equality and inequality constraints. Simulation studies demonstrate that the proposed method outperforms traditional quantile regression without constraints across various error distributions. Furthermore, we apply this method to analyze non-performing loan ratios and corn yield data, showcasing its practical applicability.</p>

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Bayesian quantile regression model with linear inequality constraints

  • 期刊论文

  • 发表日期：

    2025年5月25日

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  • Jialei Yu,
  • Jun Dai,
  • Min Xu,
  • Sami Ullah

摘要

Linear inequality constraints enhance the precision of parameter estimation by constraining parameters to a more confined space. This paper introduces a Bayesian quantile regression model with linear inequality constraints. To rigorously enforce these inequality constraints within the Bayesian framework, we adopt truncated prior distributions. Leveraging asymmetric Laplace distributions, we propose two novel Gibbs sampling methods based on truncated normal and truncated Laplace prior distributions, which involve sampling from truncated normal and generalized inverse Gaussian distributions, respectively. Our approach extends the constraints from solely inequality-based to a comprehensive framework incorporating both equality and inequality constraints. Simulation studies demonstrate that the proposed method outperforms traditional quantile regression without constraints across various error distributions. Furthermore, we apply this method to analyze non-performing loan ratios and corn yield data, showcasing its practical applicability.