SIMEX estimation for quantile regression model with measurement error

The quantile regression model with measurement error is considered. To deal with measurement error, we extend the simulation-extrapolation (SIMEX) method to the case of quantile regressions in the presence of covariate measurement error. The proposed SIMEX estimation corrects the bias caused by the measurement error, and not requires the equal distribution assumption of the regression error and measurement error. The asymptotic distribution of the pro-posed estimator is derived. The finite sample performance of the proposed method is investigated by a simulation study. A real dataset from the Framingham Heart Study is analyzed to illustrate the proposed method.