Confidence intervals for data containing many zeros and ones based on empirical likelihood-type methods

Abstract

In this paper, several existing data-driven nonparametric methods including empirical likelihood, adjusted empirical likelihood and transformed empirical likelihood are considered to construct confidence intervals for the mean of a population containing many zeros and ones. Meanwhile, we propose a transformed adjusted empirical likelihood which combines the merits of adjusted and transformed empirical likelihoods. All five methods are compared to normal approximation in terms of coverage probabilities under various scenarios through simulations. All methods are applied to three datasets to illustrate the procedure of obtaining confidence intervals.

Keywords:

• Transformed adjusted empirical likelihood
• adjusted empirical likelihood
• transformed empirical likelihood
• confidence intervals
• Coverage probability

Acknowledgments

The authors would like to thank two anonymous referees for their constructive comments and suggestions which helped to improve this manuscript significantly.

Disclosure statement

No potential conflict of interest was reported by the authors.