Extending the scope of empirical likelihood
Nils Lid Hjort, Ian W. McKeague, Ingrid Van Keilegom
The Annals of Statistics · 2009 · Volume 37 · Issue 3
Abstract
This article extends the scope of empirical likelihood methodology in three directions: to allow for plug-in estimates of nuisance parameters in estimating equations, slower than $\sqrt{n}$-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 can be used in such situations. We provide a range of examples from survival analysis and nonparametric statistics to illustrate the main results.
Keywords
62F40, 62G20, Bootstrap calibration, Current status data, Empirical processes, estimating equations, growing number of parameters, Nonparametric regression, nuisance parameters, orthogonal series, plug-in
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