Summary: In many statistical studies involving failure data, biometric mortality data, and actuarial data, mean residual lifetime (MRL) function is of prime importance. We introduce the problem of nonparametric estimation of a MRL function on an interval when this function is bounded from below by another such function (known or unknown) on that interval, and derive the corresponding two functional estimators.
The first is to be used when there is a known bound, and the second when the bound is another MRL function to be estimated independently. Both estimators are obtained by truncating the empirical estimator discussed by G. L. Yang [Ann. Stat. 6, 112-116 (1978; Zbl 0371.62055)]. In the first case, it is truncated at a known bound; in the second, at a point somewhere between the two empirical estimates. Consistency of both estimators is proved, and a pointwise large-sample distribution theory of the first estimator is derived.