Extending the scope of empirical likelihood

TL;DR

This paper broadens empirical likelihood methods to include plug-in nuisance parameter estimates, slower convergence rates, and high-dimensional estimating equations, introducing bootstrap calibration for complex scenarios.

Contribution

It extends empirical likelihood methodology to more flexible settings, including nuisance parameters with slow convergence and high-dimensional estimating equations, with bootstrap methods for calibration.

Findings

Bootstrap calibration effectively handles complex asymptotics.

Empirical likelihood applies to survival analysis and nonparametric statistics.

Method accommodates high-dimensional estimating equations.

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.