Strong Convergence Rates of the Product-limit Estimator for Left Truncated and Right Censored Data under Association

Abstract

Non-parametric estimation of a survival function from left truncated data subject to right censoring has been extensively studied in the literature. It is commonly assumed in such studies that the lifetime variables are a sample of independent and identically distributed random variables from the target population. This assumption is often prone to failure in practical studies. For instance, when recruited subjects are all from the same institute or the same geographical region. To the best of our knowledge, there is no study in the past literature addressing such situations. In this article, we study large and small sample behavior of Tsai-Jewell-Wang estimator under positive and negative association.