2017/05/23 by Peter D. Hoff, Hoff, Peter D., Chaoyu Yu +1 · 1 citation
Mathematics · #62J05 #Advanced Statistical Methods and Models #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1705.08331
openalex publication_date 2017/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.