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### 非对称误差分布的贝叶斯累加回归树模型研究及应用

1. 1. 广东财经大学统计与数学学院, 广州 510320;
2. 广东财经大学大数据与教育统计应用实 验室, 广州 510320;
3. 上海对外经贸大学统计与信息学院, 上海 201620
• 收稿日期:2021-10-09 修回日期:2022-05-29 发布日期:2022-12-13
• 通讯作者: 张日权, Email: rqzhang@suibe.edu.cn
• 基金资助:
广东省自然科学基金面上项目(2020A1515011580),国家自然科学基金面上项目(11971171) 资助课题.

CAO Taoyun, ZHANG Riquan. Research and Application of Bayesian Additive Regression Trees Model for Asymmetric Error Distribution[J]. Journal of Systems Science and Mathematical Sciences, 2022, 42(11): 3119-3133.

### Research and Application of Bayesian Additive Regression Trees Model for Asymmetric Error Distribution

CAO Taoyun1,2, ZHANG Riquan3

1. 1. School of Statistics and Mathematics, Guangdong University of Finance & Economics, Guangzhou 510320;
2. Big Data and Educationl Statistics Application Laboratory, Guangdong University of Finance and Economics, Guangzhou 510320;
3. School of Statistics and Information, Shanghai University of International Business and Economics, Shanghai 201620
• Received:2021-10-09 Revised:2022-05-29 Published:2022-12-13

Bayesian additive regression trees (BART) is a nonparametric Bayesian regression approach, which is powerful in prediction and measurement of variable importance. Assuming the random error in BART is normally distributed, this paper proposes a BART generalization model for data with asymmetric distribution. According to the tree structure of BART, we first derive asymptotic distribution for mean of response of leaves by central limit theorem. Then the asymptotic distribution of variance of response is obtained based on the property of U-statistics. The sampling iterations and parameter estimation are finally realized based on Backfitting MCMC algorithm. The results of simulation studies and comparison with random forest illustrate the feasibility and superiority of the proposed model. We finally apply the proposed model to a real data analysis.

MR(2010)主题分类:

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