Smoothing Parameters for Recursive Kernel Density Estimators under Censoring

In this paper, we are concerned with the nonparametric estimation of an unknown density under censoring. Firstly, we propose a recursive kernel density estimators under censoring, based on a stochastic approximation algorithm. Then, we showed that our recursive estimator is consistent and asymptotically normally distributed. Moreover, we describe and investigate a data-driven bandwidth selection procedure based on normal pilot bandwidth reference distributions. We showed that the proposed recursive estimators can be better than the non-recursive in terms of estimation error and much better in terms of computational costs. We corroborated these theoretical results through a simulation study and on Malaria in Senegalese children dataset.