# Exact adaptive confidence intervals for linear regression coefficients

arXiv: https://arxiv.org/abs/1705.08331 · HTML: https://mlsanity.com/paper/1705.08331/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2017.

## Built on by (most cited first, 2 of 2)

- [FAB-PPI: Frequentist, Assisted by Bayes, Prediction-Powered Inference](https://mlsanity.com/paper/2502.02363/) (2025)
- [Asymptotically Log-Optimal Bayes-Assisted Confidence Sequences for Bounded Means](https://mlsanity.com/paper/2605.07964/) (2026)

## Abstract (arXiv)

We propose an adaptive confidence interval procedure (CIP) for the coefficients in the normal linear regression model. This procedure has a frequentist coverage rate that is constant as a function of the model parameters, yet provides smaller intervals than the usual interval procedure, on average across regression coefficients. The proposed procedure is obtained by defining a class of CIPs that all have exact 1-α frequentist coverage, and then selecting from this class the procedure that minimizes a prior expected interval width. Such a procedure may be described as "frequentist, assisted by Bayes" or FAB. We describe an adaptive approach for estimating the prior distribution from the data so that exact non-asymptotic 1-α coverage is maintained. Additionally, in a "p growing with n" asymptotic scenario, this adaptive FAB procedure is asymptotically Bayes-optimal among 1-α frequentist CIPs.