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arXiv · 1705.08331

Exact adaptive confidence intervals for linear regression coefficients

Peter D. Hoff·Chaoyu Yu
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Abstract

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 $1-\alpha$ 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 $1-\alpha$ coverage is maintained. Additionally, in a "$p$ growing with $n$" asymptotic scenario, this adaptive FAB procedure is asymptotically Bayes-optimal among $1-\alpha$ frequentist CIPs.

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Peter D. Hoff, Chaoyu Yu. 2017-05-23. Exact adaptive confidence intervals for linear regression coefficients. https://arxiv.org/abs/1705.08331

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