Regression quantiles under dependent censoring

Abstract

In a recent paper, Braekers and Veraverbeke [Braekers, R. and Veraverbeke, N., 2005, A copula-graphic estimator for the conditional survival function under dependent censoring. Canadian Journal of Statistics , 33, 429–447.] obtained asymptotic results for an estimator of the conditional distribution function of the lifetime, in a fixed design regression model with dependence between lifetime and censoring time. The author complements these findings by corresponding results for the conditional quantile estimator. The main results are uniform strong consistency and a Bahadur-type representation. The latter is an invaluable tool for deriving further asymptotic results, such as the weak convergence of the quantile process.