title: Corrected-loss estimation for quantile regression with covariate measurement errors.
abstract: We study estimation in quantile regression when covariates are measured with errors. Existing methods require stringent assumptions, such as spherically symmetric joint distribution of the regression and measurement error variables, or linearity of all quantile functions, which restrict model flexibility and complicate computation. In this paper, we develop a new estimation approach based on corrected scores to account for a class of covariate measurement errors in quantile regression. The proposed method is simple to implement. Its validity requires only linearity of the particular quantile function of interest, and it requires no parametric assumptions on the regression error distributions. Finite-sample results demonstrate that the proposed estimators are more efficient than the existing methods in various models considered.
authors.affiliation: Department of Statistics, North Carolina State University, Raleigh, North Carolina 27695, U.S.A. , judy_wang@ncsu.edu.
authors.forename: Huixia Judy
authors.initials: HJ
authors.lastname: Wang
authors.forename: Leonard A
authors.initials: LA
authors.lastname: Stefanski
authors.forename: Zhongyi
authors.initials: Z
authors.lastname: Zhu
keywords: Corrected loss function; Laplace distribution; Measurement error; Normal distribution; Quantile regression; Smoothing