TWO STAGE QUANTILE REGRESSION WHEN THEFIRST STAGE IS BASED ON QUANTILEREGRESSION

We present the asymptotic properties of double-stage quantile regressionestimators with random regressors, where the first stage is based on quantile regressionswith the same quantile as in the second stage, which ensures robustness of the estimationprocedure. We derive invariance properties with respect to the reformulation of thedependent variable. We propose a consistent estimator of the variance-covariance matrixof the new estimator. Finally, we investigate finite sample properties of this estimator byusing Monte Carlo simulations.