Weak convergence of TJW product-limit estimator under association

The estimation of a survival function and its asymptotic behaviour under the random left truncation and right censor model have been extensively studied over the past few decades. In application, the assumption of independence between cases is often not true. To the best of our knowledge, there is no study in the current literature addressing weak convergence of the estimator of the survival function under this model. The current article studies the weak convergence of the Tsai-Jewell-Wang estimator under the positive or negative association, the main results of which are used to analyse a real data set.