We study varying coefficient partially linear models when some linear covariates are error-prone, but their ancillary variables are available. After calibrating the error-prone covariates, we study quantile regression estimates for parametric coefficients and nonparametric varying coefficient functions, and we develop a semiparametric composite quantile estimation procedure. Asymptotic properties of the proposed estimators are established, and the estimators achieve their best convergence rate with proper bandwidth conditions. Simulation studies are conducted to evaluate the performance of the proposed method, and a real data set is analyzed as an illustration.
"Semiparametric quantile estimation for varying coefficient partially linear measurement errors models." Braz. J. Probab. Stat. 32 (3) 616 - 656, August 2018. https://doi.org/10.1214/17-BJPS357