# Finite sample properties of the Buckland-Burnham-Augustin confidence interval centered on a model averaged estimator

## TL;DR

This paper analyzes the finite sample and asymptotic properties of a confidence interval based on a model averaged estimator in linear regression, providing exact formulas and performance insights.

## Contribution

It derives exact finite sample expressions for coverage and length of the confidence interval, advancing understanding of its performance in simple regression models.

## Key findings

- Exact finite sample coverage formulas derived.
- Performance comparison with asymptotic results.
- Insights into the interval's length and coverage behavior.

## Abstract

We consider the confidence interval centered on a frequentist model averaged estimator that was proposed by Buckland, Burnham & Augustin (1997). In the context of a simple testbed situation involving two linear regression models, we derive exact expressions for the confidence interval and then for the coverage and scaled expected length of the confidence interval. We use these measures to explore the exact finite sample performance of the Buckland-Burnham-Augustin confidence interval. We also explore the limiting asymptotic case (as the residual degrees of freedom increases) and compare our results for this case to those obtained for the asymptotic coverage of the confidence interval by Hjort & Claeskens (2003).