Consider the multiplicative censoring model given by Y i = X i U i , i =
1, . . . , n where (X i ) are i.i.d. with unknown density f on R, (U i ) are i.i.d. with uni-
form distribution U([0, 1]) and (U i ) and (X i ) are independent sequences. Only the
sample (Y i ) is observed. We study nonparametric estimators of both the density f and
the corresponding survival function F̄. First, kernel estimators are built. Pointwise risk
bounds for the quadratic risk are given, and upper and lower bounds for the rates in this
setting are provided. Then, in a global setting, a data-driven bandwidth selection pro-
cedure is proposed. The resulting estimator has been proved to be adaptive in the sense
that its risk automatically realizes the bias-variance compromise. Second, when the
X i s are nonnegative, using kernels fitted for R + -supported functions, we propose new
estimators of the survival function which are also adaptive. By simulation experiments,
we check the good performances of the estimators and compare the two strategies.

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• Nonparametric density and survival function estimation in the multiplicative censoring model