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

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 s...

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Bibliographic Details
Published in:Statistica Neerlandica 2021-08, Vol.75 (3), p.290-298
Main Authors: Wiley, Briceön, Elrod, Chris, Young, Phil D., Young, Dean M.
Format: Article
Language:English
Subjects:
average interval width
closed form
confidence interval
Confidence intervals
coverage probability
double sampling
fallible sample
infallible substudy
integrated‐likelihood‐ratio
numerical integration
underreported data
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Summary: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.
ISSN:0039-0402
1467-9574
DOI:10.1111/stan.12235