Empirical Likelihood Ratio With Arbitrarily Censored/Truncated Data by EM Algorithm

The empirical likelihood is a general nonparametric inference procedure with many desirable properties. Recently, theoretical results for empirical likelihood with certain censored/truncated data have been developed. However, the computation of empirical likelihood ratios with censored/truncated data is often nontrivial. This article proposes a modified self-consistent/EM algorithm to compute a class of empirical likelihood ratios for arbitrarily censored/truncated data with a mean type constraint. Simulations show that the chi-square approximations of the log-empirical likelihood ratio perform well. Examples and simulations are given in the following cases: (1) right-censored data with a mean parameter; and (2) left-truncated and right-censored data with a mean type parameter.