Strong representation of the Kaplan–Meier and hazard estimators for censored data with m -widely acceptable dependence

This paper investigates the asymptotic properties of the Kaplan–Meier and hazard estimators for censored survival time data. We conduct this analysis under the assumption of m-widely acceptable (m-WA) dependence, a generalized form of weak correlation. Using the Fuk–Nagaev inequality, we establish strong consistency and strong representation results for these estimators. Our findings show that the rate of strong consistency is near Formula: see text and the remainder term in the strong representation is of the same order. These results generalize and extend existing work for other types of dependent data, such as linearly extended negative quadrant-dependent (LENQD) and extended negative dependent (END) sequences, thereby broadening the theoretical foundation for these widely used statistical tools.