STATISTICAL INFERENCE FOR FOUR-REGIME SEGMENTED REGRESSION MODELS

• 成果类型: Article
• 署名作者: Yan, Han; Chen, Song Xi
• 署名单位: Peking University; Tsinghua University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/24-AOS2417
• 发表日期: 2024
• 页码: 2668-2691
• 关键词: nuisance parameter; threshold; bootstrap; selection

摘要

Segmented regression models offer model flexibility and interpretability as compared to the global parametric and the nonparametric models, and yet are challenging in both estimation and inference. We consider a four-regime segmented model for temporally dependent data with segmenting boundaries depending on multivariate covariates with nondiminishing boundary effects. A mixed integer quadratic programming algorithm is formulated to facilitate the least square estimation of the regression and the boundary parameters. The rates of convergence and the asymptotic distributions of the least square estimators are obtained for the regression and the boundary coefficients, respectively. We propose a smoothed regression bootstrap to facilitate inference on the parameters and a model selection procedure to select the most suitable model within the model class with at most four segments. Numerical simulations and a case study on air pollution in Beijing are conducted to demonstrate the proposed approach, which shows that the segmented models with three or four regimes are suitable for the modeling of the meteorological effects on the PM 2 . 5 concentration.