The strong consistency and asymptotic normality of the kernel estimator type in functional single index model in presence of censored data

In the present study, we address the nonparametric estimation challenge related to the regression function within the Single Functional Index Model in the random censoring framework. The principal achievement of this investigation lies in the establishment of the asymptotic characteristics of the estimator, including rates of almost complete convergence. Moreover, we establish the asymptotic normality of the constructed estimator under mild conditions. Subsequently, we provide the application of our findings towards the construction of confidence intervals. Lastly, we illuminate the finite-sample performance of both the model and the estimation methodology through the analysis of simulated data and a real-world data example.