Nonparametric estimation of mean residual functions

Situations frequently arise in practice in which mean residual life (mrl) functions must be ordered. For example, in a clinical trial of three experiments, let e1, e2 and e3 be the mrl functions, respectively, for the disease groups under the standard and experimental treatments, and for the disease-free group. The well-documented mrl functions e1 and e3 can be used to generate a better estimate for e2 under the mrl restriction e1 ≤ e2 ≤ e3. In this paper we propose nonparametric estimators of the mean residual life function where both upper and lower bounds are given. Small and large sample properties of the estimators are explored. Simulation study shows that the proposed estimators have uniformly smaller mean squared error compared to the unrestricted empirical mrl functions. The proposed estimators are illustrated using a real data set from a cancer clinical trial study.