Quantile Regression Estimates for a Class of Linear and Partially Linear Errors-in-Variables Models

We consider the problem of estimating quantile regression coefficients in errors-in-variables models. When the error variables for both the response and the manifest variables have a joint distribution that is spherically symmetric but otherwise unknown, the regression quantile estimates based on orthogonal residuals are shown to be consistent and asymptotically normal. We also extend the work to partially linear models when the response is related to some additional covariate.