A stochastic-fiducial-smoothing confidence interval for binomial proportions

Journal article, 2026

This study proposes a stochastic-fiducial-smoothing method for constructing binomial proportion confidence intervals (CIs), addressing the critical limitations of existing approaches in coverage accuracy and small-sample performance. Leveraging the inherent scalability of the fiducial framework, the modified fiducial (MF) approach provides enhanced statistical performance for multi-parameter inference while preserving computational tractability. In single-parameter scenarios, the MF method demonstrates competitive coverage probability and expected width (EW) compared to seven established methods: the Bayesian credibility method, the Agresti-Coull method, the likelihood ratio interval, the Blaker CI, the Clopper-Pearson method, the Jeffreys method, and the Repro sample method. In two-parameter analyses evaluating risk differences and relative risk, simulations reveal that the MF method achieves nominal confidence level stability while maintaining EWs competitive with standard fiducial method. The MF method demonstrates superior performance over the standard fiducial, providing a versatile solution for applications that require small-sample inference or complex ratio comparisons.