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An integrated‐likelihood‐ratio confidence interval for a proportion based on underreported and infallible data
Author(s) -
Wiley Briceön,
Elrod Chris,
Young Phil D.,
Young Dean M.
Publication year - 2021
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/stan.12235
Subject(s) - confidence interval , statistics , mathematics , binomial proportion confidence interval , tolerance interval , coverage probability , credible interval , sample size determination , cdf based nonparametric confidence interval , ratio estimator , estimator , robust confidence intervals , interval (graph theory) , monte carlo method , bias of an estimator , negative binomial distribution , poisson distribution , combinatorics , minimum variance unbiased estimator
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 < 0.10 or 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.