Empirical likelihood ratio with arbitrarily censored/truncated data by EM algorithm

Mai Zhou 1 University of Kentucky, Lexington, KY 40506 USA Summary. Empirical likelihood ratio method (Thomas and Grunkmier 1975, Owen 1988, 1990, 2001) is a general nonparametric inference procedure that has many nice properties. Recently the procedure has been shown to work with some censored/truncated data with various parameters. But the computation of the empirical likelihood ratios with censored/truncated data and parameter of mean is non-trivial. We propose in this paper to use a modified self-consistency/EM algorithm (Turnbull 1976) to compute a class of arbitrarily censored/truncated empirical likelihood ratios where the constraint is of mean type. Tests and confidence intervals based on the censored/truncated likelihood ratio performs well. Examples and simulations are given in the following cases: (1) right censored data with a mean parameter; (2) left truncated and right censored data with mean type parameter. AMS 1991 Subject Classification: Primary 62G10; secondary 62G05.