Estimation of low or high conditional quantiles is called for in many applications, but commonly encountered data sparsity at the tails of distributions makes this a challenging task. We develop a Bayesian joint-quantile regression method to borrow information across tail quantiles through a linear approximation of quantile coefficients. Motivated by a working likelihood linked to the asymmetric Laplace distributions, we propose a new Bayesian estimator for high quantiles by using a delayed rejection and adaptive Metropolis and Gibbs algorithm. We demonstrate through numerical studies that the proposed estimator is generally more stable and efficient than conventional methods for estimating tail quantiles, especially at small and modest sample sizes.

在许多应用中都需要对低或高条件分位数进行估计，但是在分布尾部经常遇到的数据稀疏性使这成为一项艰巨的任务。我们开发了一种贝叶斯联合分位数回归方法，以通过分位数系数的线性近似在整个尾部分位数上借用信息。受与非对称拉普拉斯分布相关的工作可能性的启发，我们通过使用延迟拒绝和自适应Metropolis和Gibbs算法，提出了一种针对高分位数的新贝叶斯估计器。通过数值研究，我们证明了拟议的估算器通常比常规的估算尾部分位数的方法更稳定，效率更高，尤其是在样本量较小且中等的情况下。