Semiparametric fiducial inference for Cox models

TL;DR

This paper introduces a new fiducial inference method tailored for semiparametric models, exemplified through the Cox proportional hazards model, showing advantages over traditional maximum likelihood estimation in certain scenarios.

Contribution

It develops the first fiducial inference framework for semiparametric models, expanding the scope of fiducial methods beyond parametric settings.

Findings

The method performs well when MLE fails.

It provides a new inference approach for Cox models.

Extensions to other models are discussed.

Abstract

R. A. Fisher introduced the fiducial distribution as a potential replacement for the Bayesian posterior distribution in the 1930s. During the past century, fiducial approaches have been explored in various parametric and nonparametric settings. However, to the best of our knowledge, no fiducial inference has been developed in the realm of semiparametric statistics. In this paper, we propose a novel fiducial approach for semiparametric models. In memory of Sir David Cox who passed away in 2022, we use the Cox proportional hazards model, which is the most popular model for the analysis of survival data, as a running example. Other models and extensions are also discussed. In our experiments, we find that our method performs particularly well in situations where the maximum likelihood estimator fails.