高维纵向数据的模型平均估计  

Model Average for High-Dimensional Longitudinal Data

作　　者：陈心洁 赵志豪 CHEN Xinjie;ZHAO Zhihao(Fareast Credit Rating Co.,Ltd.,Beijing 100007;School of Statistics,Capital University of Economics and Business,Beijing 100070;School of Mathematical Sciences,Capital Normal University,Beijing 100048)

机构地区：[1]远东资信评估有限公司,北京100007 [2]首都经济贸易大学统计学院,北京100070 [3]首都师范大学数学科学学院,北京100048

出　　处：《系统科学与数学》2020年第7期1297-1324,共28页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(11971323);首都师范大学科技创新服务能力建设-基本科研业务费(科研类)资助课题。

摘　　要：高维数据的模型选择是当今统计学研究的一个热点问题,但关于高维纵向数据方面的模型平均却少见研究,文章提出了一种利用删组交叉验证准则对高维纵向数据进行模型平均估计的方法,在最小化预测残差意义下,以删组交叉验证为准则,证明了其渐近最优性,并通过模拟研究表明,该模型平均方法在估计效果上要优于其它一些传统的模型选择和平均方法.High-dimensional model selection and model average have received much attention in recent years.However,few investigation has been conducted for the highdimensional longitudinal data.In this paper,a new model-averaging approach utilising the leave-subject-out cross-validation criterion is developed for high-dimensional longitudinal data model average.To minimize the prediction error,we estimate the model weights using a leave-subject-out cross-validation procedure.We further prove that leave-subject-out cross-validation achieves the lowest possible prediction loss asymptotically.In addition,extensive simulation studies show that the performance of the proposed model average method is much better than that of the commonly used methods.

关 键 词：模型平均 删组估计 高维纵向数据 渐近最优性 

分 类 号：O212.1[理学—概率论与数理统计]