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Modified empirical likelihood-based confidence intervals for data containing many zero observations

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Abstract

Data containing many zeroes is popular in statistical applications, such as survey data. A confidence interval based on the traditional normal approximation may lead to poor coverage probabilities, especially when the nonzero values are highly skewed and the sample size is small or moderately large. The empirical likelihood (EL), a powerful nonparametric method, was proposed to construct confidence intervals under such a scenario. However, the traditional empirical likelihood experiences the issue of under-coverage problem which causes the coverage probability of the EL-based confidence intervals to be lower than the nominal level, especially in small sample sizes. In this paper, we investigate the numerical performance of three modified versions of the EL: the adjusted empirical likelihood, the transformed empirical likelihood, and the transformed adjusted empirical likelihood for data with various sample sizes and various proportions of zero values. Asymptotic distributions of the likelihood-type statistics have been established as the standard chi-square distribution. Simulations are conducted to compare coverage probabilities with other existing methods under different distributions. Real data has been given to illustrate the procedure of constructing confidence intervals.

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Acknowledgements

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

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH, 43403, USA

    Patrick Stewart & Wei Ning

  2. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, China

    Wei Ning

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  1. Patrick Stewart
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  2. Wei Ning
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Correspondence to Wei Ning.

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Stewart, P., Ning, W. Modified empirical likelihood-based confidence intervals for data containing many zero observations. Comput Stat 35, 2019–2042 (2020). https://doi.org/10.1007/s00180-020-00993-1

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  • DOI: https://doi.org/10.1007/s00180-020-00993-1

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