Distributional Convergence under Random Censorship when Covariables are Present

Abstract

Assume that (Xi, Yi), 1 < i < n, is an i.i.d. sample of (p + 1)-variate vectors, where each Yi is at risk of being censored from the right and Xi is a vector of observable covariables. Under weak moment assumptions we show that a linear functional of the correspond- ing (p + 1)-dimensional Kaplan-Meier estimator is asymptotically normal. Applications to censored correlation, regression and mean residual lifetime estimation are discussed in greater detail.