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2019 Exact adaptive confidence intervals for linear regression coefficients
Peter Hoff, Chaoyu Yu
Electron. J. Statist. 13(1): 94-119 (2019). DOI: 10.1214/18-EJS1517

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. We describe an adaptive approach for estimating the prior distribution from the data, so that the potential risk of a poorly specified prior is reduced. The resulting adaptive confidence intervals maintain exact non-asymptotic $1-\alpha $ coverage if two conditions are met - that the design matrix is full rank (which will be known) and that the errors are normally distributed (which can be checked empirically). No assumptions on the unknown parameters are necessary to maintain exact coverage. Additionally, in a “$p$ growing with $n$” asymptotic scenario, this adaptive FAB procedure is asymptotically Bayes-optimal among $1-\alpha $ frequentist CIPs.

Citation

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Peter Hoff. Chaoyu Yu. "Exact adaptive confidence intervals for linear regression coefficients." Electron. J. Statist. 13 (1) 94 - 119, 2019. https://doi.org/10.1214/18-EJS1517

Information

Received: 1 June 2018; Published: 2019
First available in Project Euclid: 4 January 2019

zbMATH: 07003259
MathSciNet: MR3896147
Digital Object Identifier: 10.1214/18-EJS1517

Subjects:
Primary: 62J05

JOURNAL ARTICLE
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Vol.13 • No. 1 • 2019
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