It is widely pointed out in the literature that misspecification of a parametric model can lead to inconsistent estimators and wrong inference. However, even a misspecified model can provide some valuable information about the phenomena under study. This is the main idea behind the development of an approach known, in the literature, as parametrically guided nonparametric estimation. Due to its promising bias reduction property, this approach has been investigated in different frameworks such as density estimation, least squares regression and local quasi-likelihood. Our contribution is concerned with parametrically guided local quasi-likelihood estimation adapted to randomly right censored data. The generalization to censored data involves synthetic data and local linear fitting. The asymptotic properties of the guided estimator as well as its finite sample performance are studied and compared with the unguided local quasi-likelihood estimator. The results confirm the bias reduction property and show that, using an appropriate guide and an appropriate bandwidth, the proposed estimator outperforms the classical local quasi-likelihood estimator.
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