Parametrically guided nonparametric density and hazard estimation with censored data

Talamakrouni, Majda [UCL] Van Keilegom, Ingrid [UCL] El Ghouch, Anouar [UCL]

The parametrically guided kernel smoother proposed by Hjort and Glad (1995) is a promising nonparametric estimation approach that aims to reduce the bias of the classical kernel density estimator without increasing its variance. In this paper we generalize this method to the censored data case and show how it can be used for density and hazard function estimation. The asymptotic properties of the proposed estimators are established and their performance is evaluated via nite sample simulations. The method is also applied to data coming from a study where one is interested in the time to return to drug use.