The {K}aplan--{M}eier estimator as a limit function of {E}fron's self-consistency iterations

In 1967 Efron showed that the Kaplan–Meier estimator can be defined as a fixed point of a certain mapping, calling this property ``self-consistency’'. He also proposed an iterative algorithm for approximating this fixed point and suggested its convergence. The purpose of the present note is to prove this fact.