Modified estimators in semiparametric regression models with right-censored data

ABSTRACT

In this work we introduce different modified estimators for the vector parameter $\mathit{\beta }$ and an unknown regression function g in semiparametric regression models when censored response observations are replaced with synthetic data points. The main idea is to study the effects of several covariates on a response variable censored on the right by a random censoring variable with an unknown probability distribution. To provide the estimation procedure for the estimators, we extend the conventional methodology to censored semiparametric regression using different smoothing methods such as smoothing spline (SS), kernel smoothing (KS), and regression spline (RS). In addition to estimating the parameters of the semiparametric model, we also provide a bootstrap technique to make inference on the parameters. A simulation study is carried out to show the performance and efficiency properties of the estimators and analyse the effects of the different censoring levels. Finally, the performance of the estimators is evaluated by a real right-censored data set.

KEYWORDS:

• Modified estimators
• smoothing spline
• kernel smoothing
• regression spline
• right-censored data

Acknowledgements

We would like to thank the editor, the associate editor, and the anonymous referee for beneficial comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.