arXiv 16 Jun 2025 · Statistics — Methodology
arXiv:2506.13257 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Bondell, H. D., Reich, B. J., and Wang, H (2010) Noncrossing quantile regression curve estimation | 0.950 | 14 | 5 | 86% |
| 2 | Chavleishvili, S. and Manganelli, S (2024) Forecasting and stress testing with quantile vector autoregression | 0.914 | 17 | 4 | 76% |
| 3 | Jiang, L., Wang, H. J., and Bondell, H. D (2013) Interquantile shrinkage in regression models | 0.843 | 3 | 3 | 100% |
| 4 | Kohns, D. and Szendrei, T (2024) Horseshoe prior bayesian quantile regression self | 0.843 | 3 | 3 | 100% |
| 5 | Polson, N. G. and Scott, J. G (2012) On the Half-Cauchy Prior for a Global Scale Parameter | 0.843 | 3 | 3 | 100% |
| 6 | Zou, H. and Yuan, M (2008) Composite quantile regression and the oracle model selection theory | 0.811 | 4 | 2 | 100% |
| 7 | Bitto, A. and Frühwirth-Schnatter, S (2019) Achieving shrinkage in a time-varying parameter model framework | 0.737 | 5 | 3 | 40% |
| 8 | Carvalho, C. M., Polson, N. G., and Scott, J. G (2009) Handling Sparsity via the Horseshoe | 0.737 | 3 | 2 | 100% |
| 9 | Szendrei, T., Bhattacharjee, A., and Schaffer, M. E (2024) Fused LASSO as non-crossing quantile regression self | 0.737 | 3 | 2 | 100% |
| 10 | Reich, B. J. and Smith, L. B (2013) Bayesian quantile regression for censored data | 0.644 | 4 | 1 | 100% |
Showing the top 10 of 70 scored citations.
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| Citing paper | Intensity | Mentions | Sections | |
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| 1 | A Roof Over Risk: A House Price-at-Risk Framework for Hungary | 0.405 | 1 | 1 |