Data-Driven Confidence Interval Estimation Incorporating Prior Information with an Adjustment for Skewed Data

Bayesian credible interval (CI) estimation is a statistical procedure that has been well addressed in both the theoretical and applied literature. Parametric assumptions regarding baseline data distributions are critical for the implementation of this method. We provide a nonparametric technique for incorporating prior information into the equal-tailed (ET) and highest posterior density (HPD) CI estimators in the Bayesian manner. We propose to use a data-driven likelihood function, replacing the parametric likelihood function to create a distribution-free posterior. Higher order asymptotic propositions are derived to show the efficiency and consistency of the proposed method. We demonstrate that the proposed approach may correct confidence regions with respect to skewness of the data distribution. An extensive Monte Carlo (MC) study confirms the proposed method significantly outperforms the classical CI estimation in a frequentist context. A real data example related to a study of myocardial infarction illustrates the excellent applicability of the proposed technique. Supplementary material, including the R code used to implement the developed method, is available online.