An eigenfunction problem and the multivariate Kaplan-Meier estimator

Arusharka Sen

Abstract

We start with the observation that a multivariate survivor function is an eigenfunction of an integral operator given by the corresponding cumulative hazard function. This yields, under multivariate random censoring, the multivariate Kaplan-Meier estimator as a matrix eigenvector. It reduces to the familiar product-limit formula in the univariate case. We obtain the influence function of the estimator and demonstrate its efficiency. We also obtain an estimator of its asymptotic variance and present some simulation results. (This is joint work with Winfried Stute, Justus-Liebig University, Germany)