Resumen de Nonparametric density and survival function estimation in the multiplicative censoring model

Elodie Brunel, Fabienne Comte, Valentine Genon Catalot

• Consider the multiplicative censoring model given by Yi=XiUi, i=1,…,n 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) is observed. We study nonparametric estimators of both the density f and the corresponding survival function F¯. 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 Xis 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.