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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.<\/jats:p>","DOI":"10.1214\/24-aos2417","type":"journal-article","created":{"date-parts":[[2024,12,19]],"date-time":"2024-12-19T01:22:02Z","timestamp":1734571322000},"page":"2668-2691","source":"Crossref","is-referenced-by-count":4,"title":["Statistical inference for four-regime segmented regression models"],"prefix":"10.1214","volume":"52","author":[{"given":"Han","family":"Yan","sequence":"first","affiliation":[{"name":"Guanghua School of Management, Peking University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Song Xi","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Statistics and Data Science, Tsinghua University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"108","reference":[{"key":"11","doi-asserted-by":"publisher","unstructured":"Friedman, J. 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