Yang (1978) considered an empirical estimate of the mean residual life function on a fixed finite interval. She proved it to be strongly uniformly consistent and (when appropriately standardized) weakly convergent to a Gaussian process. These results are extended to the whole half line, and the variance of the the limiting process is studied. Also, nonparametric simultaneous confidence bands for the mean residual life function are obtained by transforming the limiting process to Brownian motion.
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