An algorithm for estimating threshold boundary regression models

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

Computational Statistics & Data Analysis, 2026, vol. 214, issue C

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.

Keywords: Least-squares method; Support vector machine; Weighted binary classification (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:214:y:2026:i:c:s0167947325001501

DOI: 10.1016/j.csda.2025.108274

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