Extending the scope of empirical likelihood

This article extends the scope of empirical likelihood methodology ill three directions: to allow for plug-in estimates Of nuisance parameters in estimating equations, slower than root n-rates of convergence, and settings in which there are a relatively large number of estimating equations compared to the sample size. Calibrating empirical likelihood confidence regions with plug-in is sometimes intractable due to the complexity of the asymptotics, so we introduce a bootstrap approximation that call be used in such situations. We provide a range of examples from survival analysis and nonparametric statistics to illustrate the main results.