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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 ›› 2023, Vol. 40 ›› Issue (1): 97-109.doi: 10.3969/j.issn.1005-3085.2023.01.007

• • 上一篇    下一篇

不完全观测数据下混合效应模型的正交投影估计

赵培信1,2,   张  帆1,   周小双3   

  1. 1. 重庆工商大学数学与统计学院，重庆 400067；2. 经济社会应用统计重庆市重点实验室，重庆 400067；3. 德州学院数学与大数据学院，德州 253023
  • 出版日期:2023-02-15 发布日期:2023-04-11
  • 基金资助:
    国家社科科学基金 (18BTJ035)；教育部人文社科基金 (19YJC910011)；山东省自然科学基金 (ZR2020MA021)；重庆市自然科学基金 (cstc2020jcyj-msxmX0006; cstc2021jcyj-msxmX0079).

Orthogonal Projection Based Estimation for Mixed Effects Models with Incomplete Observations

ZHAO Peixin1,2,   ZHANG Fan1,   ZHOU Xiaoshuang3   

  1. 1. School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067;
    2. Chongqing Key Laboratory of Social Economy and Applied Statistics, Chongqing 400067;
    3. College of Mathematics and Big Data, Dezhou University, Dezhou 253023
  • Online:2023-02-15 Published:2023-04-11
  • Supported by:
    The National Social Science Foundation of China (18BTJ035); the Ministry of Edu-cation Humanities and Social Sciences Research Youth Foundation (19YJC910011); the Natural Science Foundation of Shandong Province (ZR2020MA021); the Natural Science Foundation of Chongqing (cstc2020jcyj-msxmX0006; cstc2021jcyj-msxmX0079).

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摘要：

基于矩阵的 QR 分解技术，对一类含有不完全观测数据的线性混合效应模型提出了一种基于正交投影的估计方法。在一些正则条件下，证明了固定效应参数的估计渐近服从标准正态分布，得到了固定效应参数的置信区间。另外，所提出的固定效应参数的估计过程不受随机效应的任何影响，具有较好的有效性和稳健性。最后，通过一些数值模拟和一个实例分析研究了所提出估计方法的有限样本性质。

关键词: 线性混合效应模型, 正交估计, 不完全观测, 随机效应

Abstract:

Based on the QR decomposition technique, estimation method based on an orthogonal projection is proposed for a class of linear mixed effects models with incomplete observations. Under regularity conditions, the proposed estimator for fixed effects is proved to be asymptotically normal distributed, and then the confidence intervals for the fixed effects are constructed. The proposed estimator for fixed effects is not affected by the random effects, and then is more effective and robust compared with existing estimation methods. Some simulations and a real data application are also conducted for further illustrating the performances of the proposed method.

Key words: linear mixed effects model, orthogonality estimation, incomplete observations, random effects

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