Estimation of mean residual life

TL;DR

This paper extends the estimation of the mean residual life function from a fixed interval to the entire half line, providing consistency, convergence results, and confidence bands for nonparametric inference.

Contribution

It generalizes previous finite interval results to the whole half line and develops nonparametric confidence bands using Brownian motion transformations.

Findings

Strong uniform consistency of the estimator

Weak convergence to a Gaussian process

Construction of nonparametric confidence bands

Abstract

Yang (1978) considered an empirical estimate of the mean residual life function on a fixed finite interval. She proved it to be strongly uniformly consistent and (when appropriately standardized) weakly convergent to a Gaussian process. These results are extended to the whole half line, and the variance of the the limiting process is studied. Also, nonparametric simultaneous confidence bands for the mean residual life function are obtained by transforming the limiting process to Brownian motion.