Statistical inference for linear quantile regression with measurement error in covariates and nonignorable missing responses

In this paper, we consider quantile regression estimation for linear models with covariate measurement errors and nonignorable missing responses. Firstly, the influence of measurement errors is eliminated through the bias-corrected quantile loss function. To handle the identifiability issue in the nonignorable missing, a nonresponse instrument is used. Then, based on the inverse probability weighting approach, we propose a weighted bias-corrected quantile loss function that can handle both nonignorable missingness and covariate measurement errors. Under certain regularity conditions, we establish the asymptotic properties of the proposed estimators. The finite sample performance of the proposed method is illustrated by Monte Carlo simulations and an empirical data analysis.