Regression Adjustment for Noncrossing Bayesian Quantile Regression

TL;DR

This paper introduces a two-stage Bayesian quantile regression method that prevents crossing of quantile curves by applying a Gaussian process adjustment, improving accuracy and efficiency.

Contribution

It presents a novel two-stage approach combining Bayesian quantile regression with Gaussian process adjustment to ensure monotonicity and enhance performance.

Findings

The method effectively prevents quantile crossing in simulations.

It is computationally efficient compared to existing techniques.

The approach demonstrates competitive results in simulated examples.

Abstract

A two-stage approach is proposed to overcome the problem in quantile regression, where separately fitted curves for several quantiles may cross. The standard Bayesian quantile regression model is applied in the first stage, followed by a Gaussian process regression adjustment, which monotonizes the quantile function whilst borrowing strength from nearby quantiles. The two stage approach is computationally efficient, and more general than existing techniques. The method is shown to be competitive with alternative approaches via its performance in simulated examples.