Distributional convergence under proportional censorship when covariables are present (Q1273012)

When dealing with life time data censored observations may appear. In this situation efficient estimation of the survival function is given by the Kaplan-Meier product-limit estimator. An additional condition that lead the authors to the Koziol-Green model is used. The asymptotic normality for a generalized ACL (Abdushukurov-Cheng-Lin) estimator [see \textit{P. E. Cheng} and \textit{G. D. Lin}, ibid. 5, 75-80 (1987; Zbl 0629.62096)] is proved. A relation which motivates the ACL estimator is given, as well as an explicit expression for the ACL weights. This estimator has been extensively analyzed in the literature. A condition is commented and used to obtain consistent and asymptotically normal estimation under random censorship. A multivariate central limit theorem for ACL-weighted sums under an extended Koziol-Green model of proportional censorship when covariables are present is given. At the end of the paper, we find comments on some applications of the main result.