Censored depth quantiles

Quantile regression is a wide spread regression technique which allows to model the entire conditional distribution of the response variable. A natural extension to the case of censored observations was introduced by Portnoy (2003) using a reweighting scheme based on the Kaplan-Meier estimator. We apply the same ideas on the depth quantiles defined in Rousseeuw and Hubert (1999). This leads to regression quantiles for censored data which are robust to both outliers in the predictor and the response variable. For their computation, a fast algorithm over a grid of quantile values is proposed. The robustness of the method is shown in a simulation study and on two real data examples.