On nonparametric estimates of the survival function in fixed design regression model of random censoring from both sides - Abdikalikov, Farkhad; Seytaxov, Razikhakbergen (AIP conference proceedings, 2024)
We study a generalized analogue of the power estimator, studied in the works of A. Abdushukurov, for the case when observations that depend on a covariate are subject to random censoring on both sides. This nonparametric estimator for the conditional survival function at a given value of the covariate involves smoothing with Gasser-Müller weights. We establish property an almost sure asymptotic representation which provides a key tool for uniform strong consistency result. Also, this property can be used to prove the asymptotic normality and weak convergence properties of the estimate. It should also be noted that other research papers have studied a generalized analogue of the Kaplan-Meier (product-limit) estimator and the Abdushukurov-Chen-Lin (ACL) estimator in the Koziola-Green (proportional hazards) model.