Truncated composite quantile regression with covariates measurement errors

Abstract

Truncated data and measurement error data are often encountered in practice. In this paper, we study two classes of truncated composite quantile regression with covariates measured with errors. We propose weighted composite quantile regression estimators of the slope parameters based on weights which are random quantities and determined by the product-limit estimates of the distribution function of truncated variable. However, the estimators are often biased when one treats mismeasured covariates as error-free. To eliminate the bias and obtain consistent estimators, a debiasing technique is proposed. The resulting estimates are proved to be asymptotically normal and root n consistent under some mild conditions. Simulation studies and a real data example show that the proposed methods work promisingly.