Almost sure asymptotic representation for the presmoothed distribution and density estimators for censored data

摘要

Presmoothed estimation of the distribution and the density functions based on censored data is considered in this paper. A strong uniform approximation of these estimators is established. The remainder term in this approximation is also proved to be negligible in quadratic mean. As a direct consequence of these results, pointwise strong consistency and asymptotic normality for both estimators are obtained.