Hybrid confidence intervals for informative uniform asymptotic inference after model selection (2024)

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A McCloskey

Department of Economics, University of Colorado at Boulder

, Boulder, Colorado 80309,

U.S.A

adam.mccloskey@colorado.edu

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Biometrika, Volume 111, Issue 1, March 2024, Pages 109–127, https://doi.org/10.1093/biomet/asad023

Published:

24 March 2023

Article history

Published:

24 March 2023

Corrected and typeset:

07 June 2023

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Abstract

I propose a new type of confidence interval for correct asymptotic inference after using data to select a model of interest without assuming any model is correctly specified. This hybrid confidence interval is constructed by combining techniques from the selective inference and post-selection inference literatures to yield a short confidence interval across a wide range of data realizations. I show that hybrid confidence intervals have correct asymptotic coverage, uniformly over a large class of probability distributions that do not bound scaled model parameters. I illustrate the use of these confidence intervals in the problem of inference after using the lasso objective function to select a regression model of interest and provide evidence of their desirable length and coverage properties in small samples via a set of Monte Carlo experiments that entail a variety of different data distributions as well as an empirical application to the predictors of diabetes disease progression.

© The Author(s) 2023. Published by Oxford University Press on behalf of Biometrika Trust. All rights reserved. For permissions, please email: journals.permissions@oup.com

This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/pages/standard-publication-reuse-rights)

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