在线咨询
中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2026, Vol. 43 ›› Issue (1): 156-166.doi: 10.3969/j.issn.1005-3085.2026.01.010cstr: 32411.14.cjem.CN61-1269/O1.2026.01.010

• • 上一篇    下一篇

线性模型下的稳健模型平均方法

杨佳音1,  李海霞2,  常海艳2,  付利亚1,  宋亚飞3   

  1. 1. 西安交通大学数学与统计学院，西安  710049

    2. 北方自动控制技术研究所，太原 030006

    3. 空军工程大学防空反导学院，西安 710051
  • 收稿日期:2023-06-13 接受日期:2023-10-09 出版日期:2026-02-15 发布日期:2026-04-15

Robust Model Averaging Methods of Linear Model

YANG Jiayin1,  LI Haixia2,  CHANG Haiyan2,  FU Liya1,  SONG Yafei3   

  1. 1. School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049
    2. North Automatic Control Technology Institute, Taiyuan 030006
    3. Air and Missile Defense College, Air Force Engineering University, Xi'an 710051
  • Received:2023-06-13 Accepted:2023-10-09 Online:2026-02-15 Published:2026-04-15

摘要：

模型平均通过对备选模型的估计进行加权平均得到新估计，该方法具有预测精度高、风险小等优点。现有的频率模型平均方法均是基于最小二乘方法，因此对异常值比较敏感。提出了稳健的Mallows模型平均和基于信息准则的模型平均，通过选取稳健目标函数和稳健的误差标准差提升方法的稳健性。模拟研究表明数据中存在异常值或服从重尾分布时，提出的方法明显优于基于最小二乘方法的模型平均。最后，将稳健的模型平均方法应用到波士顿房价数据集上，验证了所提出方法的有效性。

关键词: 模型平均, 稳健估计, 迭代加权最小二乘, 稳健权重, 绝对中位偏差

Abstract:

The model averaging has the advantages of high prediction accuracy and low risk through the weight combination of alternative models. The existing frequency model averaging methods are all based on least square method, and thus they are sensitive to outliers. In this paper, the robust Mallows model averaging and the model averaging based on the robust information criteria are presented. This method involves the selection of robust loss functions and the robust estimation of the standard deviation of error. When there are outliers in the data or the data follow the heavy-tailed distribution, the simulation studies show that the proposed method in this paper is significantly better than the model averaging methods based on the least square method. Finally, the robust model averaging method is applied to the Boston data set.

Key words: model averaging, robust estimation, iterative weighted least squares, robust weights, median absolute deviation

中图分类号: