Beran-based approach for single-index models under censoring

In this paper we propose a new method for estimating parameters in a single-index model under censoring based on the Beran estimator for the conditional distribution function. This, likelihood-based method is also a useful and simple tool used for bandwidth selection. Additionally, we perform an extensive simulation study comparing this new Beran-based approach with other existing method based on Kaplan–Meier integrals. Finally, we apply both methods to a primary biliary cirrhosis data set and propose a bootstrap test for the parameters.