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

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  • 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
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    References listed on IDEAS

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    1. T. A. Severini, 2010. "Likelihood ratio statistics based on an integrated likelihood," Biometrika, Biometrika Trust, vol. 97(2), pages 481-496.
    2. 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.
    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.
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