Adjusted empirical likelihood with high-order precision

TL;DR

This paper introduces an adjusted empirical likelihood method that improves accuracy and guarantees solutions in small samples or high dimensions, matching Bartlett correction precision.

Contribution

The paper proposes an adjusted empirical likelihood approach that attains high-order Bartlett correction accuracy and ensures solutions to estimating equations.

Findings

Achieves high-order precision similar to Bartlett correction.

Guarantees existence of solutions to estimating equations.

Provides more accurate confidence regions in simulations.

Abstract

Empirical likelihood is a popular nonparametric or semi-parametric statistical method with many nice statistical properties. Yet when the sample size is small, or the dimension of the accompanying estimating function is high, the application of the empirical likelihood method can be hindered by low precision of the chi-square approximation and by nonexistence of solutions to the estimating equations. In this paper, we show that the adjusted empirical likelihood is effective at addressing both problems. With a specific level of adjustment, the adjusted empirical likelihood achieves the high-order precision of the Bartlett correction, in addition to the advantage of a guaranteed solution to the estimating equations. Simulation results indicate that the confidence regions constructed by the adjusted empirical likelihood have coverage probabilities comparable to or substantially more accurate than the original empirical likelihood enhanced by the Bartlett correction.