Extending the scope of empirical likelihood

Details Extending the scope of empirical likelihood Extending the scope of empirical likelihood

2009-04-20

arxiv.org/abs/0904.2949v1

Annals of Statistics 2009, Vol. 37, No. 3, 1079-1111

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/07-AOS555 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/07-AOS555

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.

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