  We consider projection methods for the estimation of the cumulative
distribution function under interval censoring, case 1. Such censored data also
known as current status data, arise when the only information available on the
variable of interest is whether it is greater or less than an observed random
time. Two types of adaptive estimators are investigated. The first one is a
two-step estimator built as a quotient estimator. The second estimator results
from a mean square regression contrast. Both estimators are proved to achieve
automatically the standard optimal rate associated with the unknown regularity
of the function, but with some restriction for the quotient estimator.
Simulation experiments are presented to illustrate and compare the methods.
