The mean residual life (mrl) function dynamically describes the average time to an event, depending on the time since the previous event. It provides a forecast in parallel with the development of the underlying process. From a theoretical point of view, the mrl characterises the distribution of the process completely, but in contrast to other characterisations like the hazard rate, it has a direct interpretation in terms of average behaviour.
We use Kaplan--Meier integrals (weighted averages of residual times) to construct a nonparametric estimator of the mrl. We use results from Stute (1995) and Yang (1994) to describe the asymptotic behaviour of this estimator and derive an approximate variance formula.
We present a small simulation study and apply the estimator (and the variance formula) to data pertaining to purchase time behaviour from the Homescan Panel^TM, A. C. Nielsen, Germany.