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Asymptotic post-selection inference for the Akaike information criterion

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  • Ali Charkhi
  • Gerda Claeskens

Abstract

SummaryIgnoring the model selection step in inference after selection is harmful. In this paper we study the asymptotic distribution of estimators after model selection using the Akaike information criterion. First, we consider the classical setting in which a true model exists and is included in the candidate set of models. We exploit the overselection property of this criterion in constructing a selection region, and we obtain the asymptotic distribution of estimators and linear combinations thereof conditional on the selected model. The limiting distribution depends on the set of competitive models and on the smallest overparameterized model. Second, we relax the assumption on the existence of a true model and obtain uniform asymptotic results. We use simulation to study the resulting post-selection distributions and to calculate confidence regions for the model parameters, and we also apply the method to a diabetes dataset.

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  • Ali Charkhi & Gerda Claeskens, 2018. "Asymptotic post-selection inference for the Akaike information criterion," Biometrika, Biometrika Trust, vol. 105(3), pages 645-664.
    • Handle: RePEc:oup:biomet:v:105:y:2018:i:3:p:645-664.
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    References listed on IDEAS

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    Cited by:

    1. Lasanthi C. R. Pelawa Watagoda & David J. Olive, 2021. "Comparing six shrinkage estimators with large sample theory and asymptotically optimal prediction intervals," Statistical Papers, Springer, vol. 62(5), pages 2407-2431, October.
    2. Rügamer, David & Baumann, Philipp F.M. & Greven, Sonja, 2022. "Selective inference for additive and linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    3. Kramlinger, Peter & Schneider, Ulrike & Krivobokova, Tatyana, 2023. "Uniformly valid inference based on the Lasso in linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    4. Jelle J Goeman & Aldo Solari, 2024. "On selection and conditioning in multiple testing and selective inference," Biometrika, Biometrika Trust, vol. 111(2), pages 393-416.
    5. Pirenne, Sarah & Claeskens, Gerda, 2024. "Exact post-selection inference for adjusted R squared selection," Statistics & Probability Letters, Elsevier, vol. 211(C).

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