Progressive censoring schemes are often adopted in clinical trials and life testing problems with a view to monitoring the experiment from the start with the objective of a possible early termination of the experiment depending on the cumulative evidence at its various stages. Along with a basic martingale property, a Wiener process approximation for progressively censored likelihood ratio statistics is established here and the same is incorporated in the formulation of some asymptotic sequential tests for the life testing problem.
"Weak Convergence of Progressively Censored Likelihood Ratio Statistics and its Role in Asymptotic Theory of Life Testing." Ann. Statist. 4 (6) 1247 - 1257, November, 1976. https://doi.org/10.1214/aos/1176343657