Robust confidence distributions from proper scoring rules

TL;DR

This paper introduces a robust method for deriving confidence distributions using proper scoring rules, particularly Tsallis scoring, to improve accuracy under model misspecification and outliers.

Contribution

It proposes a novel approach to obtain confidence distributions that are robust to data issues, extending classical methods with proper scoring rules like Tsallis.

Findings

Robust confidence distributions improve accuracy under model misspecification.

Simulation results demonstrate effectiveness in practical problems.

Method applies to two-sample tests, ROC curves, and regression models.

Abstract

A confidence distribution is a distribution for a parameter of interest based on a parametric statistical model. As such, it serves the same purpose for frequentist statisticians as a posterior distribution for Bayesians, since it allows to reach point estimates, to assess their precision, to set up tests along with measures of evidence, to derive confidence intervals, comparing the parameter of interest with other parameters from other studies, etc. A general recipe for deriving confidence distributions is based on classical pivotal quantities and their exact or approximate distributions. However, in the presence of model misspecifications or outlying values in the observed data, classical pivotal quantities, and thus confidence distributions, may be inaccurate. The aim of this paper is to discuss the derivation and application of robust confidence distributions. In particular, we discuss a general approach based on the Tsallis scoring rule in order to compute a robust confidence distribution. Examples and simulation results are discussed for some problems often encountered in practice, such as the two-sample heteroschedastic comparison, the receiver operating characteristic curves and regression models.