Consider the multiplicative censoring model given by Yi=XiUi\documentclass[12pt]{minimal}
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\begin{document}$$Y_i=X_iU_i$$\end{document}, i=1,…,n\documentclass[12pt]{minimal}
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\begin{document}$$i=1, \ldots ,n$$\end{document} where (Xi)\documentclass[12pt]{minimal}
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\begin{document}$$(X_i)$$\end{document} are i.i.d. with unknown density f on R\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {R}}$$\end{document}, (Ui)\documentclass[12pt]{minimal}
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\begin{document}$$(U_i)$$\end{document} are i.i.d. with uniform distribution U([0,1])\documentclass[12pt]{minimal}
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\begin{document}$${\mathcal {U}}([0,1])$$\end{document} and (Ui)\documentclass[12pt]{minimal}
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\begin{document}$$(U_i)$$\end{document} and (Xi)\documentclass[12pt]{minimal}
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\begin{document}$$(X_i)$$\end{document} are independent sequences. Only the sample (Yi)\documentclass[12pt]{minimal}
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\begin{document}$$(Y_i)$$\end{document} is observed. We study nonparametric estimators of both the density f and the corresponding survival function F¯\documentclass[12pt]{minimal}
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\begin{document}$$\bar{F}$$\end{document}. 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 procedure 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 Xi\documentclass[12pt]{minimal}
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\begin{document}$$X_i$$\end{document}s are nonnegative, using kernels fitted for R+\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {R}}^+$$\end{document}-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.
