Bayesian additive tree ensembles for composite quantile regressions

In this paper, we introduce a novel approach that integrates Bayesian additive regression trees (BART) with the composite quantile regression (CQR) framework , creating a robust method for modeling complex relationships between predictors and outcomes under various error distributions. Unlike traditional quantile regression, which focuses on specific quantile levels, our proposed method, composite quantile BART, offers greater flexibility in capturing the entire conditional distribution of the response variable. By leveraging the strengths of BART and CQR, the proposed method provides enhanced predic-tive performance, especially in the presence of heavy-tailed errors and non-linear covariate effects. Numerical studies confirm that composite quantile BART out-performs both standard quantile BART and CQR models across a range of scenarios.