ABSTRACT
This chapter reviews some basic convergence concepts and notations that are often used in the development of statistics theory. It introduces the counting process and martingale theories, which are the fundamental tools for deriving the asymptotic distribution of the test statistics in a survival analysis. Theorem of Slutsky is simple but very useful for deriving the asymptotic distribution of test statistics. The most fundamental result on the convergence in law is the central limit theorem. The chapter presents the finite variance case. The counting process theory for censored survival data was developed by Aalen. It plays an important role in the development of asymptotic distributions of test statistics for censored survival data, such as log-rank tests. References for the counting process theory include Counting Processes and Survival Analysis, Statistical Models Based Counting Processes, and The Statistical Analysis of Failure Time Data.
