December 2024 Statistical inference for four-regime segmented regression models
Han Yan, Song Xi Chen
Author Affiliations +
Ann. Statist. 52(6): 2668-2691 (December 2024). DOI: 10.1214/24-AOS2417

Abstract

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 PM2.5 concentration.

Funding Statement

The research was partially supported by National Natural Science Foundation of China grants 12292980, 12292983 and 92358303.

Citation

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Han Yan. Song Xi Chen. "Statistical inference for four-regime segmented regression models." Ann. Statist. 52 (6) 2668 - 2691, December 2024. https://doi.org/10.1214/24-AOS2417

Information

Received: 1 December 2023; Revised: 1 June 2024; Published: December 2024
First available in Project Euclid: 18 December 2024

Digital Object Identifier: 10.1214/24-AOS2417

Subjects:
Primary: 62H12 , 62J99
Secondary: 62F12

Keywords: mixed integer programming , segmented model , smoothed regression bootstrap , temporal dependence , threshold regression

Rights: Copyright © 2024 Institute of Mathematical Statistics

Vol.52 • No. 6 • December 2024
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