Abstract: | One of the basic parameters in survival analysis is the mean residual life M
0. For right censored observation, the usual empirical likelihood based log-likelihood ratio leads to a scaled c12{\chi_1^2} limit distribution and estimating the scaled parameter leads to lower coverage of the corresponding confidence interval.
To solve the problem, we present a log-likelihood ratio l(M
0) by methods of Murphy and van der Vaart (Ann Stat 1471–1509, 1997). The limit distribution of l(M
0) is the standard c12{\chi_1^2} distribution. Based on the limit distribution of l(M
0), the corresponding confidence interval of M
0 is constructed. Since the proof of the limit distribution does not offer a computational method for the maximization of the
log-likelihood ratio, an EM algorithm is proposed. Simulation studies support the theoretical result. |