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 predictive performance, especially in the presence of heavy-tailed errors and non-linear covariate effects. Numerical studies confirm that the proposed composite quantile BART method generally outperforms classical BART, quantile BART, and composite quantile linear regression models in terms of RMSE, especially under heavy-tailed or contaminated error distributions. Notably, under contaminated normal errors, it reduces RMSE by approximately 17% compared to composite quantile regression, and by 27% compared to classical BART.