Extended empirical likelihood for general estimating equations

TL;DR

This paper introduces an extended empirical likelihood method for parameters defined by estimating equations, enhancing accuracy and applicability while maintaining desirable asymptotic properties and data-driven shape.

Contribution

It develops a new extended empirical likelihood that covers the full parameter space and improves accuracy over existing methods.

Findings

Retains asymptotic properties of original empirical likelihood.

Achieves second order accuracy.

More accurate than existing empirical likelihood methods.

Abstract

We derive an extended empirical likelihood for parameters defined by estimating equations which generalizes the original empirical likelihood for such parameters to the full parameter space. Under mild conditions, the extended empirical likelihood has all asymptotic properties of the original empirical likelihood. Its contours retain the data-driven shape of the latter. It can also attain the second order accuracy. The first order extended empirical likelihood is easy-to-use yet it is substantially more accurate than other empirical likelihoods, including second order ones. We recommend it for practical applications of the empirical likelihood method.