Asymptotic post-selection inference for the Akaike information criterion

Ignoring 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 candi...

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Bibliographic Details
Published in:Biometrika 2018-09, Vol.105 (3), p.645-664
Main Authors: CHARKHI, ALI, CLAESKENS, GERDA
Format: Article
Language:English
Subjects:
Asymptotic properties
Computer simulation
Criteria
Diabetes mellitus
Estimators
Inference
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Summary:Ignoring 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.
ISSN:0006-3444
1464-3510
DOI:10.1093/biomet/asy018