Empirical likelihood inference for the mean residual life under random censorship

Mean residual life (MRL) for a lifetime random variable X is one of the basic parameters of interest in survival analysis. There has been a lot of work available on the inference of MRL in the complete data setting. However, the observations for X are often censored. Inference for MRL becomes more involved under random censorship. In this paper, an empirical likelihood procedure is proposed for the inference of MRL with right censored data. It is shown that the limiting distribution of the empirical log-likelihood ratio for MRL is a scaled chi-square distribution. The limiting distribution can be used to construct empirical likelihood-based confidence intervals for MRL. Numerical results from a simulation study suggest that the empirical likelihood-based confidence intervals have better coverage accuracy than the existing normal approximation-based confidence intervals.