Lim Yaeji, Lu Ruijin, Ville Madeleine St, Chen Zhen
Department of Applied Statistics, Chung-Ang University, Seoul, Korea.
Institute for Informatics, Data Science & Biostatistics, Washington University in St. Louis, Missouri, USA.
Stat Comput. 2025;35(6):175. doi: 10.1007/s11222-025-10711-w. Epub 2025 Aug 26.
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.
在本文中，我们介绍了一种新颖的方法，该方法将贝叶斯加法回归树（BART）与复合分位数回归（CQR）框架相结合，创建了一种强大的方法，用于在各种误差分布下对预测变量和结果之间的复杂关系进行建模。与专注于特定分位数水平的传统分位数回归不同，我们提出的方法——复合分位数BART，在捕捉响应变量的整个条件分布方面具有更大的灵活性。通过利用BART和CQR的优势，该方法提供了增强的预测性能，特别是在存在重尾误差和非线性协变量效应的情况下。数值研究证实，所提出的复合分位数BART方法在均方根误差（RMSE）方面通常优于经典BART、分位数BART和复合分位数线性回归模型，尤其是在重尾或受污染的误差分布下。值得注意的是，在受污染的正态误差下，与复合分位数回归相比，它将RMSE降低了约17%，与经典BART相比降低了27%。
