Weighted estimation of single index models with right censored responses

In this paper, the unknown link function, the direction parameter, and the heteroscedastic variance in single index models are estimated by the random weight method under the random censorship, respectively. The central limit theory and the convergence rate of the law of the iterated logarithm for the estimator of the direction parameter are derived, respectively. The optimal convergence rates for the estimators of the link function and the heteroscedastic variance are obtained. Simulation results support the theoretical results of the paper.