Abstract: In the random left-truncation model, one observesonly if
,
,
,
. The nonparametric maximum likelihood estimator aims at reconstructing the distribution function of
from the observed empirical data. In this paper, strong approximations of the cumulative hazard process and product-limit process on increasing sets by sequences of copies of corresponding Gaussian limiting processes are constructed. The convergence rates are
on fixed sets. Futhermore, strong approximations with two-parameter Gaussian processes are obtained with convergence rates
on fixed sets.
Key words and phrases: Cumulative hazard, Gaussian approximations, product-limit, random truncation.