  Consider a positive random variable of interest Y depending on a covariate X,
and a random observation time T independent of Y given X. Assume that the only
knowledge available about Y is its current status at time T: \delta = 1_{Y \leq
T}. This paper presents a procedure to estimate the conditional cumulative
distribution function F of Y given X from an independent identically
distributed sample of (X,T,\delta).
  A collection of finite-dimensional linear subsets of L^2(R^2) called models
are built as tensor products of classical approximation spaces of L^2(R). Then
a collection of estimators of F is constructed by minimization of a
regression-type contrast on each model and a data driven procedure allows to
choose an estimator among the collection. We show that the selected estimator
converges as fast as the best estimator in the collection up to a
multiplicative constant and is minimax over anisotropic Besov balls. Finally
simulation results illustrate the performance of the estimation and underline
parameters that impact the estimation accuracy.
