The standard asymmetric Laplace framework for Bayesian quantile regression (BQR) suffers from a fundamental decision-theoretic misalignment, yielding biased finite-sample estimates, and precludes gradient-based computation due to non-smoothness. We propose Bayesian smoothed quantile regression (BSQR), a principled framework built on a kernel-smoothed, fully differentiable likelihood. Methodologically, the symmetrizing property of our objective reduces inferential bias and aligns the posterior mean with the true conditional quantile. Theoretically, we establish posterior consistency and a Bernstein--von Mises theorem under misspecification, delivering asymptotic normality and valid frequentist coverage via a generalized Wilks phenomenon, while guaranteeing global posterior existence unlike empirical likelihood approaches. Computationally, BSQR enables Hamiltonian Monte Carlo for BQR, alleviating high-dimensional mixing bottlenecks. In simulations, BSQR reduces out-of-sample prediction error by up to 50% and improves sampling efficiency by up to 80% relative to asymmetric Laplace benchmarks, with uniform and triangular kernels performing particularly well. In a financial application to asymmetric systemic risk, BSQR uncovers distinct regime shifts around the COVID-19 period and yields sharper yet well-calibrated predictive quantiles, underscoring its practical relevance.

翻译：标准的贝叶斯分位数回归（BQR）所采用的非对称拉普拉斯框架存在根本性的决策理论失配问题，导致有限样本估计存在偏差，且因其非光滑性而无法使用基于梯度的计算方法。我们提出了贝叶斯平滑分位数回归（BSQR），这是一个建立在核平滑、完全可微似然函数基础上的原理性框架。在方法论上，我们目标函数的对称化特性减少了推断偏差，并使后验均值与真实条件分位数对齐。理论上，我们在模型设定错误的条件下建立了后验一致性及伯恩斯坦-冯·米塞斯定理，通过广义威尔克斯现象实现了渐近正态性和有效的频率学派覆盖范围，同时保证了全局后验的存在性，这一点与经验似然方法不同。在计算上，BSQR使得哈密顿蒙特卡洛方法能够应用于BQR，缓解了高维混合的瓶颈问题。在模拟实验中，相对于非对称拉普拉斯基准方法，BSQR将样本外预测误差降低了高达50%，并将采样效率提高了高达80%，其中均匀核和三角核表现尤为出色。在一项关于非对称系统性风险的金融应用中，BSQR揭示了COVID-19时期周围不同的机制转换，并产生了更尖锐且校准良好的预测分位数，突显了其实际应用价值。