Bayesian Composite Quantile Regression with Additive Regression Trees: A Robust Nonparametric Framework for Conditional Distribution Estimation

Bayesian Composite Quantile Regression with Additive Regression Trees: A Robust Nonparametric Framework for Conditional Distribution Estimation | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Bayesian Composite Quantile Regression with Additive Regression Trees: A Robust Nonparametric Framework for Conditional Distribution Estimation Samiksha Chakule, Snehal Shinde, Jagdish Chakole This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8008683/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This paper introduces a comprehensive Bayesian nonparametric framework that unifies composite quantile regression with Bayesian additive regression trees (CQR-BART). The methodology addresses fundamental limitations in conventional quantile regression by simultaneously modeling multiple quantile levels while capturing complex nonlinear relationships through tree-based ensembles. We develop a hierarchical model specification using a location-scale mixture representation of the asymmetric Laplace distribution, which enables efficient Gibbs sampling via data augmentation techniques. Key theoretical contributions include establishing posterior consistency under mild regularity conditions and proving robustness properties through bounded influence functions. Extensive simulation studies across four challenging scenarios—homoscedastic nonlinear, heteroscedastic, heavy-tailed contaminated, and high-dimensional sparse settings—demonstrate superior performance compared to existing methods in terms of estimation accuracy, uncertainty quantification, and variable selection. Practical applications to economic forecasting (Growth-at-Risk analysis) and environmental data analysis (air pollution modeling) highlight the method's utility for robust conditional distribution estimation in real-world problems. The proposed approach is implemented in an accompanying \texttt{R} package \texttt{cqrbart}, ensuring reproducibility and accessibility for applied researchers. Bayesian nonparametrics Composite quantile regression Bayesian additive regression trees MCMC sampling Robust regression Conditional distribution estimation Growth-at-Risk Environmental statistics Full Text Additional Declarations No competing interests reported. Supplementary Files Supplementarymaterial.pdf Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8008683","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":550837985,"identity":"5f127fe7-2601-445f-9187-31f384b0dce6","order_by":0,"name":"Samiksha 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sampling, Robust regression, Conditional distribution estimation, Growth-at-Risk, Environmental statistics","lastPublishedDoi":"10.21203/rs.3.rs-8008683/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8008683/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This paper introduces a comprehensive Bayesian nonparametric framework that unifies composite quantile regression with Bayesian additive regression trees (CQR-BART). The methodology addresses fundamental limitations in conventional quantile regression by simultaneously modeling multiple quantile levels while capturing complex nonlinear relationships through tree-based ensembles. We develop a hierarchical model specification using a location-scale mixture representation of the asymmetric Laplace distribution, which enables efficient Gibbs sampling via data augmentation techniques. Key theoretical contributions include establishing posterior consistency under mild regularity conditions and proving robustness properties through bounded influence functions. Extensive simulation studies across four challenging scenarios—homoscedastic nonlinear, heteroscedastic, heavy-tailed contaminated, and high-dimensional sparse settings—demonstrate superior performance compared to existing methods in terms of estimation accuracy, uncertainty quantification, and variable selection. Practical applications to economic forecasting (Growth-at-Risk analysis) and environmental data analysis (air pollution modeling) highlight the method's utility for robust conditional distribution estimation in real-world problems. 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