Censored regression quantiles

The object of this paper is to demonstrate how the LAD estimation method for the censored regression model can be extended to more general quantiles. In this paper, the form of the conditional quantiles for the censored regression models is heuristically derived and discussed. The resulting estimators of the regression coefficients, which include the censored LAD estimator as a special case, are shown to be consistent and asymptotically normally distributed under appropriately ‘translated’ versions of the corresponding assumptions for the former approach; consistent estimation of the asymptotic covariance matrix when the error terms are i.i.d. is also treated. The paper discussed how several quantile estimators might be combined to improve efficiency when the error terms are identically distributed, and how tests of homoskedasticity and symmetry of the error distribution can be constructed using particular differences of the estimated coefficients.