Estimation of the conditional distribution in a conditional Koziol-green model

We introduce a new estimator for the conditional distribution functions under the proportional hazards model of random censorship. Such estimator generalizes the one proposed by Abdushkurov, Chen and Lin when covariates are present. Asymptotic theory is given for this estimator. First, we established the strong consistency, and also obtain the rate of this convergence. Then, an asymptotic representation for the conditional distribution function estimator leads us to derive its asymptotic normality. The practical performance of the estimation procedure is illustrated on a real data set. Finally, as a further application of the new estimator, some functionals of interest in survival exploratory analysis are brieflys discussed. For the second author, this research was supported by a Human Capital postdoc fellowship, under the Programme ERB-CHRX-CT 940693.