Parametrically guided nonparametric estimation and inference with censored data

Parametrically guided nonparametric estimation is an attractive method that allows to improve the bias of a nonparametric estimator by using a parametric pilot estimator. The aim of this dissertation is to generalize the parametrically guided nonparametric estimation to randomly right-censored data. The generalization is performed in three different contexts. First, based on the Kaplan-Meier (1958) estimator, we provide new parametrically guided kernel density and hazard rate estimators. Then, we investigate the parametrically guided local linear regression and the parametrically guided quasi-likelihood estimation using a synthetic data approach. The asymptotic properties of the new-guided estimators as well as their finite sample performance are investigated and compared with the corresponding unguided nonparametric estimators via numerical studies and applications to real data. The results confirm the bias reduction property and show that using an appropriate guide and the optimal bandwidth the guided estimators outperform the classical nonparametric estimators.