Abstract:

In this paper, based on random left truncated and right censored data
 the authors derive strong representations of the cumulative hazard
function estimator and the product-limit estimator of the
survival function,
which are valid up to a given order statistic of the observations.
A precise bound for the errors is obtained which only depends on
the index of the last order statistic to be included.
Truncated and  censored data, cumulative hazard function,
product-limit estimator, strong representations

Key words: Truncated and , censored data, cumulative hazard function, product-limit estimator, strong representations