We study semiparametric varying-coefficient partially linear models when some linear covariates are not observed, but ancillary variables are available. Semiparametric profile least-square based estimation procedures are developed for parametric and nonparametric components after we calibrate the error-prone covariates. Asymptotic properties of the proposed estimators are established. We also propose the profile least-square based ratio test and Wald test to identify significant parametric and nonparametric components. To improve accuracy of the proposed tests for small or moderate sample sizes, a wild bootstrap version is also proposed to calculate the critical values. Intensive simulation experiments are conducted to illustrate the proposed approaches.
@article{1232115941,
author = {Zhou, Yong and Liang, Hua},
title = {Statistical inference for semiparametric varying-coefficient partially linear models with error-prone linear covariates},
journal = {Ann. Statist.},
volume = {37},
number = {1},
year = {2009},
pages = { 427-458},
language = {en},
url = {http://dml.mathdoc.fr/item/1232115941}
}
Zhou, Yong; Liang, Hua. Statistical inference for semiparametric varying-coefficient partially linear models with error-prone linear covariates. Ann. Statist., Tome 37 (2009) no. 1, pp. 427-458. http://gdmltest.u-ga.fr/item/1232115941/