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《山东大学学报(理学版)》 ›› 2026, Vol. 61 ›› Issue (9): 23-34.doi: 10.6040/j.issn.1671-9352.0.2024.309

• • 上一篇    

基于指数平方函数的纵向数据回归模型稀疏稳健估计

程雨荷1,2,张宾1,2*   

  1. 1.广西师范大学数学与统计学院, 广西 桂林 541006;2.广西师范大学广西高校数据科学交叉研究重点实验室, 广西 桂林 541006
  • 发布日期:2026-09-30
  • 通讯作者: 张宾(1984— ),男,讲师,博士,研究方向为纵向数据模型的统计推断及应用. E-mail:binzhang@gxnu.edu.cn
  • 作者简介:程雨荷(2000— ),女,硕士研究生,研究方向为纵向数据统计建模及推断. E-mail:yuhecheng@stu.gxnu.edu.cn*通信作者:张宾(1984— ),男,讲师,博士,研究方向为纵向数据模型的统计推断及应用. E-mail:binzhang@gxnu.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(12461099);广西科技基地和人才专项资助项目(桂科AD23026220);广西自然科学基金项目(2025GXNSFAA069225)

Sparse and robust estimation of longitudinal data regression models based on the exponential squared function

CHENG Yuhe1,2, ZHANG Bin1,2*   

  1. 1. School of Mathematics and Statistics, Guangxi Normal University, Guilin 541006, Guangxi, China;
    2. Key Laboratory of Interdisciplinary Research for Data Science, Guangxi Normal University, Guilin 541006, Guangxi, China
  • Published:2026-09-30

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摘要： 首先,利用指数平方函数构造新的得分函数,实现回归参数的稳健估计。其次,对经验似然函数进行平滑剪裁绝对偏差惩罚,使均值和协方差矩阵估计同时具备稀疏性与稳健性的良好统计性质,并给出求解该模型的牛顿迭代算法。最后,证明参数估计的渐近正态性,并通过数值模拟将本文的估计方法与现有的方法进行比较。结果表明在不同协方差结构和误差分布下,本文方法在稳健性和稀疏性方面均表现出更优越的性能。

关键词: 纵向数据模型, 稳健估计, 经验似然估计, 指数平方函数, 稀疏性

Abstract: First, the exponential squared function is used to construct a new score function to achieve a robust estimation of the regression parameters. Second, the empirical likelihood function is penalized by the smoothly clipped absolute deviation, so that the mean and covariance matrix estimates simultaneously possess good statistical properties of sparsity and robustness. Additionally, a Newton-Raphson iterative algorithm for solving the model is provided. Finally, the asymptotic normality of the parameter estimators is proved, and the proposed method is compared with existing methods through numerical simulations, demonstrating superior performance in terms of robustness and sparsity across different covariance structures and error distributions.

Key words: longitudinal data model, robust estimation, empirical likelihood estimation, exponential squared function, sparsity

中图分类号: 

  • O212
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