  We propose a new class of semiparametric regression models of mean residual
life for censored outcome data. The models, which enable us to estimate the
expected remaining survival time and generalize commonly used mean residual
life models, also conduct covariate dimension reduction. Using the geometric
approaches in semiparametrics literature and the martingale properties with
survival data, we propose a flexible inference procedure that relaxes the
parametric assumptions on the dependence of mean residual life on covariates
and how long a patient has lived. We show that the estimators for the covariate
effects are root-$n$ consistent, asymptotically normal, and semiparametrically
efficient. With the unspecified mean residual life function, we provide a
nonparametric estimator for predicting the residual life of a given subject,
and establish the root-$n$ consistency and asymptotic normality for this
estimator. Numerical experiments are conducted to illustrate the feasibility of
the proposed estimators. We apply the method to analyze a national kidney
transplantation dataset to further demonstrate the utility of the work.
