Local Unbiasedness of Confidence Intervals for a Binomial Proportion

Abstract

A confidence interval is unbiased if the probability of covering the true parameter is no lessthan the probability of false coverage. In the binomial distribution, a nonrandom confidence interval for abinomial proportion may not be unbiased, but it can satisfy local unbiasedness within specific regions of theparameter space. In this study, we propose a method to determine these regions of local unbiasedness. Byapplying this methodology, we either confirm the unbiasedness of existing confidence intervals or identifythe regions where local unbiasedness holds. Additionally, we define the locally unbiased ratio as the totallength of these regions divided by the length of the parameter space. Using the locally unbiased ratio as acriterion, we compare the performance of existing intervals and provide recommendations based on ourfindings.

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