均值模型中基于稳健变量选择的多变点估计

Multiple Change-Point Estimation in Mean Models Based on Robust Variable Selection

摘要: 基于变量选择的多变点估计是目前数据研究的热点问题，而数据中异常值的存在往往会严重干扰变点估计的精度与稳定性，基于稳健变量选择的多变点估计成为该领域亟待解决的问题。文章提出一种带有指数平方损失函数(Exponential Squared Loss, ESL)的两阶段多变点估计方法，结合调节参数对惩罚力度的灵活控制，实现了对数据中异常值的有效抵御，具备良好的稳健性。数值模拟结果表明，在含有1%、5%、10%异常值的场景下，基于指数平方损失的两阶段多变点估计方法均优于累积和方法和基于平方损失函数的两阶段多变点估计方法。应用R语言自带的测井数据进行实证分析，验证了该方法的有效性。该方法为含有异常值数据的稳健变点估计提供了有效的新思路，可为相关实际应用提供重要的方法支撑与参考。

Abstract: Multiple change-point estimation based on variable selection is a hot topic in current data research. However, the presence of outliers in data often severely interferes with the accuracy and stability of change-point estimation. Therefore, multiple change-point estimation based on robust variable selection has become an urgent problem to be solved in this field. This paper proposes a two-stage multiple change-point estimation method with the Exponential Squared Loss (ESL) function. By flexibly controlling the penalty intensity through tuning parameters, this method effectively resists outliers in the data and exhibits excellent robustness. Numerical simulation results show that the proposed two-stage method based on exponential squared loss outperforms both the cumulative sum (CUSUM) method and the two-stage multiple change-point estimation method based on the squared loss function in scenarios with 1%, 5%, and 10% outliers. Empirical analysis is conducted using the well-log data built into R, which verifies the effectiveness of the method. This method provides a new effective idea for robust change-point estimation of data containing outliers, and can offer important methodological support and reference for relevant practical applications.