  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.
