15 A guide to censored quantile regressions

Abstract

Publisher Summary This chapter discusses the concept of censored quantile regression (CQR) estimator. While a least squares regression models, the conditional mean of some explained variable as a function of regressors, it is often also of interest to model conditional quantiles. In the case without censoring, this can be done by estimating quantile regressions—regression quantiles, as they are often called—that were introduced by Koenker and Bassett. Powell developed CQR's as a robust extension to the censored regression problem. The potential advantages of CQR compared to standard treatments of the censored regression problem are twofold. First, CQR's are an alternative to simply modeling conditional means—that is, they can distinguish among differential effects across conditional quantiles. Second, they allow for consistent estimation of the censored regression model under far less distributional assumptions than commonly required. Naturally, the robustness of CQR's comes with a cost in situations where the distributional assumptions for maximum likelihood are satisfied. The treatment in the chapter is restricted to the case of CQR's in the linear regression context but conceptually CQR's could also be used for nonlinear models.