@article{88b56b1e391444848fac03a3f6c56507,
title = "Estimation and inference of error-prone covariate effect in the presence of confounding variables",
abstract = "We introduce a general single index semiparametric measurement error model for the case that the main covariate of interest is measured with error and modeled parametrically, and where there are many other variables also important to the modeling. We propose a semiparametric bias-correction approach to estimate the effect of the covariate of interest. The resultant estimators are shown to be root-n consistent, asymptotically normal and locally efficient. Comprehensive simulations and an analysis of an empirical data set are performed to demonstrate the finite sample performance and the bias reduction of the locally efficient estimators.",
keywords = "Confounding effect, Measurement error, Primary effect, Semiparametric efficiency, Single index model",
author = "Jianxuan Liu and Yanyuan Ma and Liping Zhu and Carroll, {Raymond J.}",
note = "Funding Information: Ma{\textquoteright}s research was supported by a grant from the NSFCNational Natural Science Foundation (DMS-1608540). Zhu is the corresponding author and his research was supported by grants from the National Natural Science Foundation of ChinaNSFC (11371236 and 11422107), the MOE Project of Key Research Institute of Humanities and Social Sciences at Universities (16JJD910002) and National Youth Top-notch Talent Support Program, China. Carroll{\textquoteright}s research was supported by a grant from the National Cancer Institute (U01-CA057030). Ma{\textquoteright}s research was supported by a grant from the National Natural Science Foundation (DMS-1608540). Zhu is the corresponding author and his research was supported by grants from the National Natural Science Foundation of China (11371236 and 11422107), the MOE Project of Key Research Institute of Humanities and Social Sciences at Universities (16JJD910002) and National Youth Top-notch Talent Support Program, China. Carroll{\textquoteright}s research was supported by a grant from the National Cancer Institute (U01-CA057030). Publisher Copyright: {\textcopyright} 2017, Institute of Mathematical Statistics. All rights reserved.",
year = "2017",
doi = "10.1214/17-EJS1242",
language = "English (US)",
volume = "11",
pages = "480--501",
journal = "Electronic Journal of Statistics",
issn = "1935-7524",
publisher = "Institute of Mathematical Statistics",
number = "1",
}