IDEAS home Printed from https://ideas.repec.org/a/bla/stanee/v75y2021i3p290-298.html
   My bibliography  Save this article

An integrated‐likelihood‐ratio confidence interval for a proportion based on underreported and infallible data

Author

Listed:
  • Briceön Wiley
  • Chris Elrod
  • Phil D. Young
  • Dean M. Young

Abstract

We derive and examine the interval width and coverage properties of an integrated‐likelihood‐ratio confidence interval for the binomial parameter p using a double‐sampling scheme. The data consist of a relatively large fallible sample containing underreported data and a relatively small infallible subsample. Via Monte Carlo simulations, we determine that the new integrated‐likelihood‐ratio interval estimator displays slightly conservative to moderately conservative coverage properties for small to medium sample sizes and can have shorter average‐interval width than two previously proposed confidence intervals when p 0.90. We also apply the integrated‐likelihood‐ratio confidence interval to a real‐data set and determine that the integrated‐likelihood‐ratio interval has superior performance when contrasted to two properties of two competing confidence intervals.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:stanee:v:75:y:2021:i:3:p:290-298
    DOI: 10.1111/stan.12235
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/stan.12235
    Download Restriction: no
    File URL: https://libkey.io/10.1111/stan.12235?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. T. A. Severini, 2010. "Likelihood ratio statistics based on an integrated likelihood," Biometrika, Biometrika Trust, vol. 97(2), pages 481-496.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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.
    4. Dewi Rahardja, 2019. "Bayesian Inference for the Difference of Two Proportion Parameters in Over-Reported Two-Sample Binomial Data Using the Doubly Sample," Stats, MDPI, vol. 2(1), pages 1-10, February.
    5. Giuliana Cortese & Nicola Sartori, 2016. "Integrated likelihoods in parametric survival models for highly clustered censored data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(3), pages 382-404, July.
    6. Tang, Man-Lai & Qiu, Shi-Fang & Poon, Wai-Yin, 2012. "Confidence interval construction for disease prevalence based on partial validation series," Computational Statistics & Data Analysis, Elsevier, vol. 56(5), pages 1200-1220.
    7. H. V. Kulkarni & S. M. Patil, 2021. "Uniformly implementable small sample integrated likelihood ratio test for one-way and two-way ANOVA under heteroscedasticity and normality," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(2), pages 273-305, June.
    8. Thomas A. Severini, 2023. "Integrated likelihood inference in multinomial distributions," METRON, Springer;Sapienza Università di Roma, vol. 81(2), pages 131-142, August.
    9. Dewi Rahardja, 2022. "Omnibus Tests for Multiple Binomial Proportions via Doubly Sampled Framework with Under-Reported Data," Stats, MDPI, vol. 5(2), pages 1-14, April.
    10. Stamey, James D. & Boese, Doyle H. & Young, Dean M., 2008. "Confidence intervals for parameters of two diagnostic tests in the absence of a gold standard," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1335-1346, January.
    11. Rahardja, Dewi & Young, Dean M., 2010. "Credible sets for risk ratios in over-reported two-sample binomial data using the double-sampling scheme," Computational Statistics & Data Analysis, Elsevier, vol. 54(5), pages 1281-1287, May.
    12. 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.
    13. Ruggero Bellio & Annamaria Guolo, 2016. "Integrated Likelihood Inference in Small Sample Meta-analysis for Continuous Outcomes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 191-201, March.
    14. Zhenyu Zhao & Thomas A. Severini, 2017. "Integrated likelihood computation methods," Computational Statistics, Springer, vol. 32(1), pages 281-313, March.
    15. 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.
    16. Zaigraev, A. & Podraza-Karakulska, A., 2014. "Maximum integrated likelihood estimator of the interest parameter when the nuisance parameter is location or scale," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 99-106.
    17. Rahardja, Dewi & Young, Dean M., 2011. "Likelihood-based confidence intervals for the risk ratio using double sampling with over-reported binary data," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 813-823, January.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:stanee:v:75:y:2021:i:3:p:290-298. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0039-0402 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.