Pyramid quantile regression

TL;DR

This paper introduces a Bayesian nonparametric approach using quantile pyramids for simultaneous linear quantile regression, effectively capturing complex conditional distributions and outperforming existing methods, especially for extremal quantiles.

Contribution

It proposes a novel Bayesian framework with quantile pyramids for flexible, nonparametric quantile regression that allows meaningful prior specification and handles diverse scenarios.

Findings

Outperforms existing methods in simulation studies

Effective in modeling extremal quantiles

Applicable to real data with linear splines and extreme value analysis

Abstract

Quantile regression models provide a wide picture of the conditional distributions of the response variable by capturing the effect of the covariates at different quantile levels. In most applications, the parametric form of those conditional distributions is unknown and varies across the covariate space, so fitting the given quantile levels simultaneously without relying on parametric assumptions is crucial. In this work we propose a Bayesian model for simultaneous linear quantile regression. More specifically, we propose to model the conditional distributions by using random probability measures known as quantile pyramids. Unlike many existing approaches, our framework allows us to specify meaningful priors on the conditional distributions, whilst 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. The method is particularly promising for modelling the extremal quantiles. Applications to linear splines and extreme value analysis are also explored through real data examples.