Probability inequalities governing the approximation of the basic martingale, the rescaled difference between a counting process and its compensator, are derived. Applications to the random censoring model and to the field of goodness-of-fit tests are given. The inequalities are compared to inequalities derived earlier for the random censoring model using an empirical process approach.
"Approximation of the Basic Martingale." Ann. Statist. 22 (2) 565 - 579, June, 1994. https://doi.org/10.1214/aos/1176325485