Bernstein polynomial of recursive regression estimation with censored data

Abstract

In this paper, we deal with the problem of the regression estimation near the edges under censoring. For this purpose, we consider a new recursive estimator based on the stochastic approximation algorithm and Bernstein polynomials of the regression function when the response random variable is subject to random right censoring. We give the central limit theorem and the strong pointwise convergence rate for our proposed nonparametric recursive estimators under some mild conditions. Finally, we provide pointwise moderate deviation principles (MDP) for the proposed estimators. We corroborate these theoretical results through simulations as well as the analysis of a real data set.