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

Author

Listed:
  • Patrick Stewart

    (Bowling Green State University)

  • Wei Ning

    (Bowling Green State University
    Beijing Institute of Technology)

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.

Suggested Citation

  • Patrick Stewart & Wei Ning, 2020. "Modified empirical likelihood-based confidence intervals for data containing many zero observations," Computational Statistics, Springer, vol. 35(4), pages 2019-2042, December.
    • Handle: RePEc:spr:compst:v:35:y:2020:i:4:d:10.1007_s00180-020-00993-1
    DOI: 10.1007/s00180-020-00993-1
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    References listed on IDEAS

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    3. Kvanli, Alan H & Shen, Yaung Kaung & Deng, Lih Yuan, 1998. "Construction of Confidence Intervals for the Mean of a Population Containing Many Zero Values," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 362-368, July.
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    6. Xiao-Hua Zhou & Wanzhu Tu, 2000. "Confidence Intervals for the Mean of Diagnostic Test Charge Data Containing Zeros," Biometrics, The International Biometric Society, vol. 56(4), pages 1118-1125, December.
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