Reformulating Confidence as Extended Likelihood

TL;DR

This paper introduces a new extended-likelihood framework for confidence, based on Fisher's fiducial probability, which addresses longstanding controversies and improves asymptotic confidence estimates for multi-dimensional parameters.

Contribution

It reformulates confidence as extended likelihood, enabling multi-dimensional analysis and higher-order approximation techniques to refine confidence statements.

Findings

Framework resolves long-standing controversies in confidence estimation.

Accommodates multi-dimensional parameters effectively.

Enhances asymptotic confidence with higher-order approximations.

Abstract

Fisher's fiducial probability has recently received renewed attention under the name confidence. In this paper, we reformulate it within an extended-likelihood framework, a representation that helps to resolve many long-standing controversies. The proposed formulation accommodates multi-dimensional parameters and shows how higher-order approximations can be used to refine standard asymptotic confidence statements.