Let (X, Y ) be a random vector, where Y denotes the variable of interest possibly subject to random right censoring, and X is a covariate. The variable Y is a (possible monotone transformation of a) survival time. The censoring time C and the survival time Y are allowed to be dependent, and the dependence is described via a known copula (this also includes the independent case). Under this setting we propose estimators of certain location and scale functionals of Y given X. We derive their asymptoticproperties, uniformly over the support of X. In particular we derive an asymptotic representation and the uniform convergence rates for these estimators and their derivatives. We also prove asymptotic results for an estimator of the conditional distribution (the so-called conditional copula-graphic estimator), which generalizes previous results obtained by Braekers and Veraverbeke (2005). We also illustrate the results via simulations and the analysis of data on bone marrow transplantation.
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