Smooth estimation of mean residual life under random censoring

TL;DR

This paper introduces a new smooth estimator for the mean residual life function in the presence of random censoring, improving boundary bias issues and establishing its statistical properties.

Contribution

It develops a boundary bias-free smoothing technique for censored data and analyzes its asymptotic behavior, extending previous methods from complete data to censored data.

Findings

The estimator is strongly uniformly consistent.

It is asymptotically normal.

Properties are similar to those in complete data cases.

Abstract

We propose here a smooth estimator of the mean residual life function based on randomly censored data. This is derived by smoothing the product-limit estimator using the Chaubey-Sen technique (Chaubey and Sen (1998)). The resulting estimator does not suffer from boundary bias as is the case with standard kernel smoothing. The asymptotic properties of the estimator are investigated. We establish strong uniform consistency and asymptotic normality. This complements the work of Chaubey and Sen (1999) which considered a similar estimation procedure in the case of complete data. It is seen that the properties are similar, though technically more difficult to prove, to those in the complete data case with appropriate modifications due to censoring.