Nonparametric Estimation of Mean Residual Life Function Using Scale Mixtures

It is often of interest in clinical trials and reliability studies to estimate the remaining lifetime of a subject or a device given that it survived up to a given period of time, that is commonly known as the so-called mean residual life function (mrlf). There have been several attempts in literature to estimate the mrlf nonparametrically ranging from empirical estimates to more sophisticated smooth estimation. Given the well known one-to-one relation between survival function and mrlf, one can plug-in any known estimates of the survival function (e.g., Kaplan–Meier estimate) into the functional form of mrlf to obtain an estimate of mrlf. In this chapter, we present a scale mixture representation of mrlf and use it to obtain a smooth estimate of the mrlf under right censoring. Asymptotic properties of the proposed estimator are also presented. Several simulation studies and a real data set are used for investigating the empirical performance of the proposed method relative to other well-known estimates of mrlf. A comparative analysis shows computational advantages of the proposed estimator in addition to somewhat superior statistical properties in terms of bias and efficiency.