Nonparametric interval estimation for the mean of a zero-inflated population

Abstract

In many statistical analysis, data may consist of excess zero values and the non-zero values are highly positively skewed. Confidence intervals based on a normal approximation for such zero-inflated data may have low coverage probabilities. An empirical likelihood (EL) and adjusted empirical likelihood methods are proposed to construct a non-parametric confidence interval for the mean of zero-inflated population, which are very simple and easy to implement. These EL confidence intervals were compared with existing confidence intervals. Simulation studies are carried out. Finally, the method is implemented in a real data set.

Keywords:

• Empirical likelihood
• Adjusted empirical likelihood
• Health data
• Zero values
• Skewed distribution
• Wilk’s theorem

Acknowledgments

The authors would like to thank the Editor-in-Chief, an associate editor and two reviewers for the useful comments and constructive suggestions, which improve the presentation of the manuscript.

Additional information

Funding

Yichuan Zhao acknowledges the support from both NSA Grant (H98230-12-1-0209) and NSF Grant (DMS-1613176).