Nonparametric local linear estimation of the relative error regression function for censorship model

TL;DR

This paper introduces a new nonparametric local linear estimator for the relative error regression function in censored data, demonstrating its consistency and asymptotic properties through simulations.

Contribution

It develops a novel estimator using mean squared relative error for censored data, with proven consistency and simulation validation.

Findings

Estimator is uniformly almost surely consistent.

Simulation results confirm the asymptotic behavior.

Method effectively handles right censoring in regression analysis.

Abstract

In this paper, we built a new nonparametric regression estimator with the local linear method by using the mean squared relative error as a loss function when the data are subject to random right censoring. We establish the uniform almost sure consistency with rate over a compact set of the proposed estimator. Some simulations are given to show the asymptotic behavior of the estimate in different cases.