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An algorithm for estimating threshold boundary regression models

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  • Chang, Chih-Hao
  • Emura, Takeshi
  • Huang, Shih-Feng

Abstract

This paper presents an innovative iterative two-stage algorithm designed for estimating threshold boundary regression (TBR) models. By transforming the non-differentiable least-squares (LS) problem inherent in fitting TBR models into an optimization framework, our algorithm combines the optimization of a weighted classification error function for the threshold model with obtaining LS estimators for regression models. To improve the efficiency and flexibility of TBR model estimation, we integrate the weighted support vector machine (WSVM) as a surrogate method for solving the weighted classification problem. The TBR-WSVM algorithm offers several key advantages over recently developed methods: it eliminates pre-specification requirements for threshold parameters, accommodates flexible estimation of nonlinear threshold boundaries, and streamlines the estimation process. We conducted several simulation studies to illustrate the finite-sample performance of TBR-WSVM. Finally, we demonstrate the practical applicability of the TBR model through a real data analysis.

Suggested Citation

  • Chang, Chih-Hao & Emura, Takeshi & Huang, Shih-Feng, 2026. "An algorithm for estimating threshold boundary regression models," Computational Statistics & Data Analysis, Elsevier, vol. 214(C).
    • Handle: RePEc:eee:csdana:v:214:y:2026:i:c:s0167947325001501
    DOI: 10.1016/j.csda.2025.108274
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