Despite the practicality of quantile regression (QR), simultaneous estimation of multiple QR curves continues to be challenging. We address this problem by proposing a Bayesian nonparametric framework that generalizes the quantile pyramid by replacing each scalar variate in the quantile pyramid with a stochastic process on a covariate space. We propose a novel approach to show the existence of a quantile pyramid for all quantiles. The process of dependent quantile pyramids allows for non-linear QR and automatically ensures non-crossing of QR curves on the covariate space. Simulation studies document the performance and robustness of our approach. An application to cyclone intensity data is presented.

翻译：尽管分位数回归（QR）具有实用性，但多个QR曲线的同时估计仍具挑战性。我们通过提出一种贝叶斯非参数框架来解决此问题，该框架将分位数金字塔中的每个标量变量替换为协变量空间上的随机过程，从而推广了分位数金字塔。我们提出了一种新方法来证明所有分位数下分位数金字塔的存在性。依赖分位数金字塔过程允许非线性分位数回归，并自动确保协变量空间上分位数回归曲线不相交。模拟研究证明了我们方法的性能与稳健性。最后，我们展示了该模型在台风强度数据中的应用。