@article{Xiao2023, 
author = {Yanting Xiao and Wanying Dong},
title = {Robust estimation for varying-coefficient partially linear measurement error model with auxiliary instrumental variables},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {8},
pages = {18373-18391},
keywords = {modal regression, auxiliary variables, varying-coefficient partially linear models, error-in-variable},
url = {https://www.sciopen.com/article/10.3934/math.2023934},
doi = {10.3934/math.2023934},
abstract = {We study the varying-coefficient partially linear model when some linear covariates are not observed, but their auxiliary instrumental variables are available. Combining the calibrated error-prone covariates and modal regression, we present a two-stage efficient estimation procedure, which is robust against outliers or heavy-tail error distributions. Asymptotic properties of the resulting estimators are established. Performance of our proposed estimation procedure is illustrated through some numerous simulations and a real example. And the results confirm that the proposed methods are satisfactory.}
}