Asymptotic Inference for Dependent Right-Censored Data via Markov Models

Abstract

In survival analysis and reliability theory, the assumption of independent lifetimes is often violated in real-world systems. This paper develops a version of the central limit theorem (CLT) for rightcensored lifetime data in which the failure times follow a first-order Markov process with a geometric transition structure. We provide theoretical justification for the asymptotic normality of a functional of the Kaplan-Meier estimator under these dependent conditions, derive the variance of the limiting distribution, and validate our findings with simulation studies.