Resumen
This paper deals with smooth estimation of two survival functions (SFs), S1 and S2 subject to the mean residual life (MRL) ordering, i.e. subject to M1?M2, where M1 and M2 denote the MRLs corresponding to S1 and S2, respectively. This is achieved by smooth estimation of the two MRLs, M1 and M2 subject to M1?M2 and obtaining the corresponding SFs. Two estimators are provided: one using the (non-smooth) estimator of Hu et al. [2002. Estimation of two ordered mean residual life functions. J. Statist. Plann. Inference 107, 321–341] and another utilizing the “uniform stochastic ordering” (USO) of ?x?Si(u)du, i=1,2, and the technique of the (non-smooth) estimation of Rojo and Samaniego [1993. On estimating a survival curve subject to a uniform stochastic ordering constraint. J. Amer. Statist. Assoc. 88, 566–572] of the two SFs ordered by USO.