Empirical likelihood for mean difference between two samples with missing data

Abstract

In this paper, we consider the empirical likelihood confidence intervals for mean difference under the assumption of missing at random (MAR). We prove that the empirical log-likelihood ratio of mean difference converges to a standard chi-squared distribution. We conduct simulation study to compare the proposed empirical likelihood with the normal approximation method in terms of the coverage accuracies and average lengths of confidence intervals. By Monte Carlo simulations, we verify that the proposed method performs well.

KEYWORDS:

• Empirical likelihood
• Mean difference
• Missing at random
• Standard chi-squared distribution

MATHEMATICAL SUBJECT CLASSIFICATION:

• 62D10
• 62G05

Acknowledgments

We are very grateful to the referees for their most interesting comments and suggestions.

Additional information

Funding

This study was partially supported by the National Key R&D Program of China (No. 2018YFA0703900), the National Natural Science Foundation of China (Nos. 11871309 and 11371226) and the Natural Science Foundation of Shandong Province (No. ZR2019MA035).