Pyramid Quantile Regression

Abstract

We describe a Bayesian model for simultaneous linear quantile regression at several specified quantile levels. More specifically, we propose to model the conditional distributions by using random probability measures, known as quantile pyramids, introduced by Hjort and Walker. Unlike many existing approaches, this framework allows us to specify meaningful priors on the conditional distributions, while retaining the flexibility afforded by the nonparametric error distribution formulation. Simulation studies demonstrate the flexibility of the proposed approach in estimating diverse scenarios, generally outperforming other competitive methods. We also provide conditions for posterior consistency. The method is particularly promising for modeling the extremal quantiles. Applications to extreme value analysis and in higher dimensions are also explored through data examples. Supplemental material for this article is available online.

Keywords:

• Bayesian quantile pyramid
• Extremal quantile regression
• Simultaneous quantile regression

Additional information

Funding

TR is funded by CAPES Foundation via the Science Without Borders (BEX 0979/13-9). TR and YF are grateful to the Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers for support.