Joint Quantile Shrinkage: A State-Space Approach toward Non-Crossing Bayesian Quantile Models

TL;DR

This paper introduces a Bayesian framework for quantile regression that prevents crossing of quantile curves by jointly estimating multiple quantiles with a fused shrinkage prior, resulting in improved accuracy and predictive performance.

Contribution

It proposes a novel state-space Bayesian model with a fused shrinkage prior for non-crossing quantile estimation, integrating a TVP-inspired approach.

Findings

Outperforms existing methods in simulated experiments

Provides better parameter recovery and predictive accuracy

Demonstrates effectiveness in macroeconomic data analysis

Abstract

Crossing of fitted conditional quantiles is a prevalent problem for quantile regression models. We propose a new Bayesian modelling framework that penalises multiple quantile regression functions toward the desired non-crossing space. We achieve this by estimating multiple quantiles jointly with a prior on variation across quantiles, a fused shrinkage prior with quantile adaptivity. The posterior is derived from a decision-theoretic general Bayes perspective, whose form yields a natural state-space interpretation aligned with Time-Varying Parameter (TVP) models. Taken together our approach leads to a Quantile-Varying Parameter (QVP) model, for which we develop efficient sampling algorithms. We demonstrate that our proposed modelling framework provides superior parameter recovery and predictive performance compared to competing Bayesian and frequentist quantile regression estimators in simulated experiments and a real-data application to multivariate quantile estimation in macroeconomics.