基于逆概率加权和插补的Mallows模型平均方法

doi:10.12341/jssms21363

系统科学与数学 ›› 2022, Vol. 42 ›› Issue (4): 1032-1059.DOI: 10.12341/jssms21363

基于逆概率加权和插补的Mallows模型平均方法

祝恒坤¹, 张海丽²

1. 首都师范大学数学科学学院北京 100048;
2. 南方科技大学统计与数据科学系深圳 518055

收稿日期:2021-07-05 修回日期:2021-12-04 出版日期:2022-04-25 发布日期:2022-06-18
通讯作者: 祝恒坤,Email:hengkunzhu@163.com.
基金资助:
国家自然科学基金(12031016,11971323),首都师范大学交叉科学研究院和生物统计交叉学科资助课题.

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祝恒坤, 张海丽. 基于逆概率加权和插补的Mallows模型平均方法[J]. 系统科学与数学, 2022, 42(4): 1032-1059.

ZHU Hengkun, ZHANG Haili. Mallows Model Averaging Based on Inverse Probability Weighting and Imputation[J]. Journal of Systems Science and Mathematical Sciences, 2022, 42(4): 1032-1059.

Mallows Model Averaging Based on Inverse Probability Weighting and Imputation

ZHU Hengkun¹, ZHANG Haili²

1. School of Mathematical Sciences, Capital Normal University, Beijing 100048;
2. Department of Statistics and Data Science, Southern University of Science and Technology, Shenzhen 51805

Received:2021-07-05 Revised:2021-12-04 Online:2022-04-25 Published:2022-06-18

关键词： 非随机缺失, 插补, 逆概率加权, 模型平均, 渐近最优性

Missing data is a common issue in real data analysis. In this paper, we combine the inverse probability weighting method with the imputation method and propose a Mallows model averaging method for missing data. We prove that the proposed method asymptotically achieves the lowest possible squared error. Compared with the traditional inverse probability weighting method, the proposed method can not only take full information provided by the training data but also be applied to data under missing not at random. Our method also inherits some advantages of the imputation method and avoids the bias caused by the erroneous imputation of large data blocks. Simulation results show that three common imputation methods satisfy the condition where the asymptotic optimality is established and the proposed method is superior to some existing model averaging methods applied to missing data. We also use the proposed method to life expectancy data.

Key words: Missing not at random, imputation, inverse probability weighting, model averaging, asymptotic optimality

MR(2010)主题分类:

62F12
62J05

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