Strong consistency of presmoothed Kaplan-Meier integrals when covariables are present

It is known that the Kaplan-Meier estimation may be improved via presmoothing methods. In this article, we introduce an extended presmoothed Kaplan-Meier estimator in the presence of covariates. The main result is the strong consistency of general empirical integrals based on such an estimator. As applications, one can obtain a consistent multivariate empirical distribution under censoring, and also can obtain a consistent estimation of regression parameters. We illustrate the new estimation methods through simulations and real data analysis.