Simultaneous adjustment of bias and coverage probabilities for confidence intervals

We give a method for the correction of confidence intervals when the original interval does not have the correct nominal coverage probabilities in the frequentist sense. Our method is general and does not require any distributional assumptions. It can be applied to both frequentist and Bayesian inference where interval estimates are desired. We provide theoretical results for the consistency of our proposed estimator, and provide two complex examples, on confidence interval correction for composite likelihood estimators and in approximate Bayesian computation, to demonstrate the wide applicability of our method.