Simultaneous adjustment of bias and coverage probabilities for confidence intervals

TL;DR

This paper introduces a general, assumption-free method to correct confidence intervals, ensuring accurate coverage probabilities in both frequentist and Bayesian contexts, demonstrated through complex examples and comparisons with existing techniques.

Contribution

It presents a novel, distribution-free approach for adjusting confidence intervals to achieve correct coverage, applicable to various inference methods including composite likelihood and ABC.

Findings

Method achieves consistent coverage correction.

Applicable to both frequentist and Bayesian intervals.

Outperforms some existing correction techniques.

Abstract

A new method is proposed for the correction of confidence intervals when the original interval does not have the correct nominal coverage probabilities in the frequentist sense. The proposed 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 the proposed estimator, and give two complex examples, on confidence interval correction for composite likelihood estimators and in approximate Bayesian computation (ABC), to demonstrate the wide applicability of the new method. Comparison is made with the double-bootstrap and other methods of improving confidence interval coverage.