Abstract
In this paper, we consider the multiplicative censoring model, given by Yi = XiUi where (Xi) are i.i.d. with unknown density f on R, (Ui) are i.i.d. with uniform distribution U([0, 1]) and (Ui) and (Xi) are independent sequences. Only the sample (Yi) 1≤i≤n is observed. Nonparametric estimators of both the density f and the corresponding survival function ¯ F are proposed and studied. First, classical kernels are used and the estimators are studied from several points of view: pointwise risk bounds for the quadratic risk are given, upper and lower bounds for the rates in this setting are provided. Then, an adaptive non asymptotic bandwidth selection procedure in a global setting is proved to realize the bias-variance compromise in an automatic way. When the Xi's are nonnegative, using kernels fitted for R +-supported functions, we propose new estimators of the survival function which are proved to be adaptive. Simulation experiments allow us to check the good performances of the estimators and compare the two strategies.