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

2025-06-16

AI Summary

Quantile crossing—the violation of monotonicity in conditional quantile functions—is a persistent issue in quantile regression. Method: This paper proposes a state-space-based Bayesian joint quantile modeling framework. It introduces a quantile-varying-parameter (QVP) model that embeds non-crossing constraints directly into the prior structure; employs a fused shrinkage prior to adaptively regularize variability across multiple quantile functions; and derives the posterior from a generalized Bayesian decision-theoretic perspective, yielding a natural state-space interpretation. The approach incorporates time-varying parameter extensions and a customized MCMC algorithm. Contribution/Results: Simulation studies and multivariate quantile forecasting experiments in macroeconomics demonstrate substantial improvements in parameter recovery accuracy and out-of-sample predictive performance, consistently surpassing state-of-the-art Bayesian and frequentist quantile regression methods.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs

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.

Problem

• Prevents crossing of fitted conditional quantiles in regression
• Proposes Bayesian framework with non-crossing quantile penalties
• Improves parameter recovery and predictive performance in quantile estimation

Innovation

• Bayesian framework penalizes quantile crossing
• Fused shrinkage prior with quantile adaptivity
• Efficient sampling for QVP model