Boundary-free Estimators of the Mean Residual Life Function by Transformation

TL;DR

This paper introduces two boundary-free kernel estimators for the mean residual life function that effectively address boundary bias issues using bijective transformations, preserving the mean value property.

Contribution

The paper presents novel boundary-free kernel estimators for the mean residual life function utilizing bijective transformations, improving bias correction and property preservation.

Findings

Estimators perform well in simulations.

Real data analysis confirms effectiveness.

Boundary bias is significantly reduced.

Abstract

We propose two new kernel-type estimators of the mean residual life function $m_X(t)$ of bounded or half-bounded interval supported distributions. Though not as severe as the boundary problems in the kernel density estimation, eliminating the boundary bias problems that occur in the naive kernel estimator of the mean residual life function is needed. In this article, we utilize the property of bijective transformation. Furthermore, our proposed methods preserve the mean value property, which cannot be done by the naive kernel estimator. Some simulation results showing the estimators' performances and a real data analysis will be presented in the last part of this article.