An algorithm for estimating threshold boundary regression models

IF 1.6 3区数学 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computational Statistics & Data Analysis Pub Date : 2025-09-15 DOI:10.1016/j.csda.2025.108274

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

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引用次数: 0

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.

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估计阈值边界回归模型的算法

提出了一种新的阈值边界回归（TBR）模型估计迭代两阶段算法。该算法通过将TBR模型拟合中固有的不可微最小二乘问题转化为优化框架，将阈值模型的加权分类误差函数优化与回归模型的LS估计相结合。为了提高TBR模型估计的效率和灵活性，我们将加权支持向量机（WSVM）作为替代方法来解决加权分类问题。与最近开发的方法相比，TBR-WSVM算法提供了几个关键优势：它消除了对阈值参数的预规范要求，适应非线性阈值边界的灵活估计，并简化了估计过程。我们进行了一些仿真研究来说明TBR-WSVM的有限样本性能。最后，通过实际数据分析，验证了TBR模型的实用性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computational Statistics & Data Analysis 数学-计算机：跨学科应用

CiteScore

3.70

自引率

5.60%

发文量

167

审稿时长

60 days

期刊介绍： Computational Statistics and Data Analysis (CSDA), an Official Publication of the network Computational and Methodological Statistics (CMStatistics) and of the International Association for Statistical Computing (IASC), is an international journal dedicated to the dissemination of methodological research and applications in the areas of computational statistics and data analysis. The journal consists of four refereed sections which are divided into the following subject areas: I) Computational Statistics - Manuscripts dealing with: 1) the explicit impact of computers on statistical methodology (e.g., Bayesian computing, bioinformatics,computer graphics, computer intensive inferential methods, data exploration, data mining, expert systems, heuristics, knowledge based systems, machine learning, neural networks, numerical and optimization methods, parallel computing, statistical databases, statistical systems), and 2) the development, evaluation and validation of statistical software and algorithms. Software and algorithms can be submitted with manuscripts and will be stored together with the online article. II) Statistical Methodology for Data Analysis - Manuscripts dealing with novel and original data analytical strategies and methodologies applied in biostatistics (design and analytic methods for clinical trials, epidemiological studies, statistical genetics, or genetic/environmental interactions), chemometrics, classification, data exploration, density estimation, design of experiments, environmetrics, education, image analysis, marketing, model free data exploration, pattern recognition, psychometrics, statistical physics, image processing, robust procedures. [...] III) Special Applications - [...] IV) Annals of Statistical Data Science [...]