工具变量辅助的变系数测量误差模型的估计

doi:10.7523/j.issn.2095-6134.2018.01.001

中国科学院大学学报 ›› 2018, Vol. 35 ›› Issue (1): 1-9.DOI: 10.7523/j.issn.2095-6134.2018.01.001

• 数学与物理学 • 下一篇

工具变量辅助的变系数测量误差模型的估计

刘智凡¹, 王妙妙², 谢田法², 孙志华^1,3

1. 中国科学院大学数学科学学院, 北京 100049;
2. 北京工业大学应用数理学院, 北京 100124;
3. 中国科学院大数据挖掘与知识管理重点实验室, 北京 100049

收稿日期:2016-10-11 修回日期:2017-02-28 发布日期:2018-01-15
通讯作者: 孙志华
基金资助:
国家自然科学基金（11231010，11571340，U1430103）和中国科学院大数据挖掘与知识管理重点实验室开放课题资助

Estimation of error-in-variable varying-coefficient model with auxiliary instrument variables

LIU Zhifan¹, WANG Miaomiao², XIE Tianfa², SUN Zhihua^1,3

1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;
2. College of Applied Sciences, Beijing University of Technology, Beijing 100124, China;
3. Key Laboratory of Big Data Mining and Knowledge Management of Chinese Academy of Sciences, Beijing 100049, China

Received:2016-10-11 Revised:2017-02-28 Published:2018-01-15

摘要/Abstract

摘要： 考虑协变量有测量误差时变系数模型的估计问题。提出的方法不需要假定特定的误差模型结构或已知的误差方差，也不需要重复观测的数据。通过工具变量的辅助，首先对测量误差进行校正，从而得到真实观察变量的估计。然后用这个估计取代真实观察变量，利用变系数模型的估计方法得到函数系数的估计。证明了所提估计的渐近正态性。数值模拟结果表明本文提出的基于校正误差的方法比直接使用测量误差数据的方法有更好的有限样本性质。

关键词: 变系数模型, 测量误差, 工具变量, 校正误差, 渐近正态性

Abstract: In this work, we consider the estimation of the variable-coefficient model when the covariates are measured with error. We do not specify any model structure of the measurement error, and do not require the knowledge of the variance of measurement error. Furthermore, repeated measurement data are not necessary. With the help of the instrument variable, we calibrate the error and obtain an estimator of the true variable. We replace the true variable by its estimator and get an estimator of the coefficient function by applying the local linear smoothing method. We prove the asymptotic normality of the proposed estimator. The simulation results show that the proposed estimator performs better than the naive estimator.

Key words: variable-coefficient model, measurement error, instrument variable, error calibration, asymptotic normality

中图分类号:

O212.7

刘智凡, 王妙妙, 谢田法, 孙志华. 工具变量辅助的变系数测量误差模型的估计[J]. 中国科学院大学学报, 2018, 35(1): 1-9.

LIU Zhifan, WANG Miaomiao, XIE Tianfa, SUN Zhihua. Estimation of error-in-variable varying-coefficient model with auxiliary instrument variables[J]. , 2018, 35(1): 1-9.

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工具变量辅助的变系数测量误差模型的估计

Estimation of error-in-variable varying-coefficient model with auxiliary instrument variables

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