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，但同时对多条分位数曲线进行估计仍具挑战性。本文通过提出一种贝叶斯非参数框架来解决这一问题，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方法。我们提出了一种新颖的方法，证明了所有分位数上分位数金字塔的存在性。相依分位数金字塔过程支持非线性分位数回归，并自动确保协变量空间上分位数曲线不发生交叉。仿真研究验证了我们方法的性能与稳健性。最后，我们将其应用于台风强度数据分析。