A0682
Title: An objective length-based evaluation for binomial confidence intervals
Authors: Chung-Han Lee - National Cheng Kung University (Taiwan) [presenting]
Zong-Lin Lin - National Yang Ming Chiao Tung University (Taiwan)
Abstract: Evaluating the performance of a confidence interval based solely on its length is inherently subjective. Although the lengths of two intervals can be objectively compared under equal coverage probability, this condition is rarely satisfied for binomial confidence intervals, where coverage probability varies with the true parameter. As a result, comparing interval lengths across different methods often lacks true objectivity due to coverage discrepancies. To address this limitation, an objective, length-based evaluation criterion for binomial confidence intervals is proposed. Specifically, the concept of local unbiasedness is applied to interval length evaluation, providing a new framework for objectively assessing confidence intervals. The locally unbiased ratio is defined as the proportion of the parameter space where local unbiasedness holds. Using the locally unbiased ratio as a criterion, existing binomial confidence intervals are evaluated, and recommendations are provided based on the findings.
