Consistent Estimation Under Random Censorship When Covariables Are Present

Assume that (Xi, Yi), 1 ≤ i ≤ n, are independent (p + 1)-variate vectors, where each Yi is at risk of being censored from the right and Xi is a vector of observable covariables. We introduce a (p + 1)-dimensional extension of the Kaplan-Meier estimator and show its consistency. Also a general strong law for Kaplan-Meier integrals is proved, which, e.g., may be utilized to prove consistency of a new regression parameter estimator under random censorship.