On the strong uniform consistency for relative error of the regression function estimator for censoring times series model

TL;DR

This paper investigates the uniform almost sure consistency of a kernel estimator for the relative error regression function in a censored, dependent data setting, providing theoretical results and simulation validation.

Contribution

It establishes the uniform almost sure consistency with rate for the kernel estimator under dependence and censoring, highlighting the covariance term's role.

Findings

Estimator performs well in finite samples

Consistency results hold under $\alpha$-mixing dependence

Simulation confirms theoretical properties

Abstract

Consider a random vector (X, T), where X is d-dimensional and T is one-dimensional. We suppose that the random variable T is subject to random right censoring and satisfies the $\alpha$-mixing property. The aim of this paper is to study the behavior of the kernel estimator of the relative error regression and to establish its uniform almost sure consistency with rate. Furthermore, we have highlighted the covariance term which measures the dependency. The simulation study shows that the proposed estimator performs well for a finite sample size in different cases.