Random sets and exact confidence regions

TL;DR

This paper introduces a novel method using random sets to construct exact confidence regions in statistics, avoiding reliance on asymptotic approximations and ensuring precise coverage probabilities.

Contribution

It proposes a new approach with random sets that guarantees exact confidence regions, a significant improvement over traditional asymptotic methods.

Findings

Confidence regions with exact coverage probability

Use of random sets satisfying a validity property

Construction of data-dependent plausibility functions

Abstract

An important problem in statistics is the construction of confidence regions for unknown parameters. In most cases, asymptotic distribution theory is used to construct confidence regions, so any coverage probability claims only hold approximately, for large samples. This paper describes a new approach, using random sets, which allows users to construct exact confidence regions without appeal to asymptotic theory. In particular, if the user-specified random set satisfies a certain validity property, confidence regions obtained by thresholding the induced data-dependent plausibility function are shown to have the desired coverage probability.