Likelihood ratio inference for mean residual life

One of the basic parameters in survival analysis is the mean residual life M0. For right censored observation, the usual empirical likelihood based log-likelihood ratio leads to a scaled \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\chi_1^2}$$\end{document} 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(M0) by methods of Murphy and van der Vaart (Ann Stat 1471–1509, 1997). The limit distribution of l(M0) is the standard \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\chi_1^2}$$\end{document} distribution. Based on the limit distribution of l(M0), the corresponding confidence interval of M0 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.