Abstract: In this paper, we consider the Tsai-Jewel-Wang estimatorof an unknown distribution function
when the data are subject to random left truncation and right censorship. Strong Gaussian approximations of the product-limit process
are constructed with rate
. A functional law of the iterated logarithm for the maximal deviation of the estimator from the estimand is derived from the construction.
Key words and phrases: Cumulative hazard, left truncation, Gaussian approximations, right censorship, product-limit.