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

doi:10.7523/j.issn.2095-6134.2018.01.001

›› 2018, Vol. 35 ›› Issue (1): 1-9.DOI: 10.7523/j.issn.2095-6134.2018.01.001

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 Online:2018-01-15

Abstract

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

CLC Number:

O212.7

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

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