A note on the two-sample mean problem based on jackknife empirical likelihood

ABSTRACT

In this article, we employ the jackknife empirical likelihood (JEL) method to construct the confidence regions for the difference of the means of two d-dimensional samples. Compared with traditional EL for the two-sample mean problem, JEL is extremely simpler to use in practice and is more effective in computing. Based on the JEL ratio test, a version of Wilks’ theorem is developed. Furthermore, to improve the coverage accuracy of confidence regions, a Bartlett correction is applied. The effectiveness of the proposed method is demonstrated by a simulation study and a real data analysis.

KEYWORDS:

• Bartlett correction
• coverage accuracy
• jackknife empirical likelihood
• two-sample problem

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G15
• 62G20

Funding

This work is supported by the National Natural Science Foundation of China (11401561, 11571340), and the open project of Hubei Collaborative Innovation Center for Early Warning and Emergency Response Technology (JD20150402).