  In this paper we propose an automatic bandwidth selection of the recursive
kernel density estimators with missing data in the context of global and local
density estimation. We showed that, using the selected bandwidth and a special
stepsize, the proposed recursive estimators outperformed the nonrecursive one
in terms of estimation error in the case of global estimation. However, the
recursive estimators are much better in terms of computational costs. We
corroborated these theoretical results through simulation studies and on the
simulated data of the Aquitaine cohort of HIV-1 infected patients and on the
coriell cell lines using the chromosome number 11.
