ABSTRACT
In many applications, data are imperfectly collected. Variables are often measured with error and data are missing for various reasons. Regression calibration is often a simple solution to correct measurement error bias for mean regressions. The measurement error-induced bias could be corrected by solving the corrected estimating equations, as in, or, equivalently, by minimizing a corrected quantile regression loss function. As for the mean regression calibration approach designed to correct measurement errors, simple conditional mean imputation is only valid when the estimation equations are linear, but that is not the case for quantile regression. Likewise, ignoring missing observations in the data can lead to efficiency loss or biased estimation. While there is an abundant literature on measurement errors and missing data, there have been little attention devoted to quantile methods directly, primarily due to the lack of parametric likelihood in quantile regression. Ignoring the missing data will undermine study efficiency and sometimes introduce substantial bias.
