纵向数据下存在测量误差的单指标模型的估计及应用  

A New Estimation for Single Index Model with Longitudinal Data in the Presence of Measurement Errors

作　　者：林红梅 张少东 彭宜洛 杜金艳 LIN Hongmei;ZHANG Shaodong;PENG Yiluo;DU Jinyan(School of Statistics and Information,Shanghai University of International Business and Economics,Shanghai,201620,China)

机构地区：[1]上海对外经贸大学统计与信息学院,上海201620

出　　处：《应用概率统计》2023年第4期561-576,共16页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金面上项目(批准号:12171310);上海市自然科学基金面上项目(批准号:20ZR1421800);2022年度“曙光计划”自然科学类项目(批准号:22SG52);统计与数据科学前沿理论及应用教育部重点实验室(华东师范大学)项目资助。

摘　　要：纵向数据是一类在社会学、经济学、生物医学、传染病学等领域有着广泛应用的重要的数据类型.然而在实际问题中,人们会经常遇到变量维数很高且关心的变量不能直接观测也即存在测量误差的情形.为了解决此类问题,本文研究存在测量误差的纵向数据下单指标模型的估计问题.基于局部线性光滑法和模拟外推(SIMEX)法,本文构造了估计单指标参数和非参连接函数的新方法.通过蒙特卡罗数值模拟验证所提估计方法的有效性,与忽略测量误差的Naive估计以及忽略个体内部相关性的估计相比,本文所构造的估计具有更小的均方误差.最后,我们将本文方法应用到上市公司投资需求的实际数据分析中,结果表明在实际问题中测量误差对参数估计影响显著.Longitudinal data is an important type of data that is widely used in sociology,economics,biomedicine,epidemiology and other fields.However,in practical problems,people often encounter the situation that the variable dimension is very high and the variable concerned cannot be directly observed,that is,there is a measurement error.In order to solve such problems,this paper studies the estimation of the longitudinal data order index model with measurement error.Based on local linear method and simulation extrapolation(SIMEX)method,this paper constructs a new method for estimating singleindex parameters and nonparametric link functions.The effectiveness of the proposed estimation method is verified by Monte Carlo numerical simulation.Compared with the Naive estimation which ignores the measurement error and the estimation which ignores the intra-individual correlation,the estimation constructed in this paper has a smaller mean square error.Finally,we apply the method in this paper to the actual data analysis of the investment demand of listed companies,and the results show that the measurement error has a significant impact on the parameter estimation in practical problems.

关 键 词：单指标模型 纵向数据 测量误差 局部线性估计 SIMEX法 

分 类 号：O212.1[理学—概率论与数理统计]