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Model selection and inference: facts and fiction. (English) Zbl 1085.62004
Summary: Model selection has an important impact on subsequent inference. Ignoring the model selection step leads to invalid inference. We discuss some intricate aspects of data-driven model selection that do not seem to have been widely appreciated in the literature. We debunk some myths about model selection, in particular the myth that consistent model selection has no effect on subsequent inference asymptotically. We also discuss an “impossibility” result regarding the estimation of the finite-sample distribution of post-model-selection estimators.

MSC:
62A01 Foundations and philosophical topics in statistics
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