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.

Keywords:

• Asymptotic convergence
• Bernstein polynomial
• censored data
• nonparametric regression estimation
• stochastic approximation algorithm

Acknowledgements

The author is indebted to the Editor-in-Chief of Stochastic Models, Prof. Mark Squillante, the associate Editor and the two anonymous reviewers for their very valuable comments and suggestions which led to a considerable improvement of the manuscript. To my father Azzam Slaoui, to whom I promised to dedicate this work before he left this world.