Situations occur frequently in which the mean residual life (mrl) functions of
two populations are ordered. For example, if a mechanical device is improved,
the mrl function for the improved device should not be less than that of the
original device. Also, mrl functions for medical patients should often be ordered
depending on the status of concomitant variables. We propose nonparametric estimators
of the bivariate mrl function under a mean residual life ordering. The estimators
are shown to be asymptotically unbiased, strongly uniformly consistent and weakly
convergent to a bivariate Gaussian process on closed finite rectangles.

Key words and phrases: Survival function, Mean residual life function, Mean residual
life ordering, Asymptotic properties, Admissibility, Loss function.