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Maximum likelihood estimation of a binomial proportion using one-sample misclassified binary data

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  • Dewi Rahardja
  • Ying Yang

Abstract

type="main"> In this article, we construct two likelihood-based confidence intervals (CIs) for a binomial proportion parameter using a double-sampling scheme with misclassified binary data. We utilize an easy-to-implement closed-form algorithm to obtain maximum likelihood estimators of the model parameters by maximizing the full-likelihood function. The two CIs are a naïve Wald interval and a modified Wald interval. Using simulations, we assess and compare the coverage probabilities and average widths of our two CIs. Finally, we conclude that the modified Wald interval, unlike the naïve Wald interval, produces close-to-nominal CIs under various simulations and, thus, is preferred in practice. Utilizing the expressions derived, we also illustrate our two CIs for a binomial proportion parameter using real-data example.

Suggested Citation

  • Dewi Rahardja & Ying Yang, 2015. "Maximum likelihood estimation of a binomial proportion using one-sample misclassified binary data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(3), pages 272-280, August.
    • Handle: RePEc:bla:stanee:v:69:y:2015:i:3:p:272-280
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    File URL: http://hdl.handle.net/10.1111/stan.12058
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    References listed on IDEAS

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    1. Boese, Doyle H. & Young, Dean M. & Stamey, James D., 2006. "Confidence intervals for a binomial parameter based on binary data subject to false-positive misclassification," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3369-3385, August.
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    Cited by:

    1. Partha Lahiri & Noriah M. Al-Kandari, 2016. "Prediction of a Function of Misclassified Binary Data," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 17(3), pages 429-447, September.
    2. Al-Kandari Noriah M. & Lahiri Partha, 2016. "Prediction of a Function of Misclassified Binary Data," Statistics in Transition New Series, Polish Statistical Association, vol. 17(3), pages 429-447, September.
    3. Noriah M. Al-Kandari & Partha Lahiri, 2016. "Prediction Of A Function Of Misclassified Binary Data," Statistics in Transition New Series, Polish Statistical Association, vol. 17(3), pages 429-447, September.
    4. Briceön Wiley & Chris Elrod & Phil D. Young & Dean M. Young, 2021. "An integrated‐likelihood‐ratio confidence interval for a proportion based on underreported and infallible data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(3), pages 290-298, August.
    5. Dewi Rahardja, 2020. "Multiple Comparison Procedures for the Differences of Proportion Parameters in Over-Reported Multiple-Sample Binomial Data," Stats, MDPI, vol. 3(1), pages 1-12, March.

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