Statistical Inference for Four-Regime Segmented Regression Models

TL;DR

This paper develops a novel four-regime segmented regression model for temporally dependent data with multivariate covariates, providing estimation, inference, and model selection methods, demonstrated through simulations and air pollution case study.

Contribution

It introduces a mixed integer quadratic programming approach for estimation and a bootstrap method for inference in four-regime segmented models with non-diminishing boundary effects.

Findings

Segmented models with three or four regimes fit air pollution data well.

The proposed methods achieve consistent estimation and valid inference.

Numerical simulations confirm the effectiveness of the approach.

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 non-diminishing 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.