Bartlett-corrected two-sample adjusted empirical likelihood via resampling

ABSTRACT

To construct confidence regions for the difference of two population means, Liu and Yu (2010) proposed a two-sample adjusted empirical likelihood (AEL) with high-order precision. However, two issues have not been well addressed. The first one is that the AEL ratio function is bounded such that the size of the confidence regions may overly expand when the sample sizes are small and/or the dimension of data is large. The second issue is that its high-order precision relies on accurate estimation of the Bartlett factor, while accurately estimating the Bartlett factor is a serious challenge. In order to address these two problems simultaneously, we propose a two-sample modified AEL to ensure the boundedness of confidence regions and preserve the Bartlett correctability. A two-stage procedure is proposed for constructing accurate confidence regions via resampling. The finite-sample performance of the proposed method is illustrated by simulations and a real-data example.

KEYWORDS:

• Adjusted empirical likelihood
• Bartlett correction
• bootstrap
• coverage probability
• empty set problem
• two-sample empirical likelihood

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G05
• 62G10
• 62G20
• 62G35

Acknowledgments

The author would like to thank the editor, the associate editor, and two anonymous referees for numerous insightful comments and suggestions, which have led to significant improvements.

Funding

This work was supported by the Postdoctoral Science Foundation of China (2014M560317), National Natural Science Foundation of China (11501208, 11371142, 11271135), and the Chinese 111 Project grant B14019.