On Bayesian quantile regression curve fitting via auxiliary variables

TL;DR

This paper introduces a Bayesian auxiliary variable approach for quantile regression curve fitting, particularly using splines with unknown knots, offering an efficient algorithm and solutions for crossing quantile curves.

Contribution

It adapts auxiliary variable methods to Bayesian quantile regression, enabling flexible spline fitting with automated tuning and addressing crossing issues.

Findings

Effective algorithm with fully automated tuning.

Successful application on simulated and real data.

Extension to additive models demonstrated.

Abstract

Quantile regression has received increased attention in the statistics community in recent years. This article adapts an auxiliary variable method, commonly used in Bayesian variable selection for mean regression models, to the fitting of quantile regression curves. We focus on the fitting of regression splines, with unknown number and location of knots. We provide an efficient algorithm with Metropolis-Hastings updates whose tuning is fully automated. The method is tested on simulated and real examples and its extension to additive models is described. Finally we propose a simple postprocessing procedure to deal with the problem of the crossing of multiple separately estimated quantile curves.