Can One Estimate the Unconditional Distribution of Post-Model-Selection Estimators ?

Hannes Leeb () and Benedikt Pötscher

MPRA Paper from University Library of Munich, Germany

Abstract: We consider the problem of estimating the unconditional distribution of a post-model-selection estimator. The notion of a post-model-selection estimator here refers to the combined procedure resulting from first selecting a model (e.g., by a model selection criterion like AIC or by a hypothesis testing procedure) and then estimating the parameters in the selected model (e.g., by least-squares or maximum likelihood), all based on the same data set. We show that it is impossible to estimate the unconditional distribution with reasonable accuracy even asymptotically. In particular, we show that no estimator for this distribution can be uniformly consistent (not even locally). This follows as a corollary to (local) minimax lower bounds on the performance of estimators for the distribution. These lower bounds are shown to approach 1/2 or even 1 in large samples, depending on the situation considered. Similar impossibility results are also obtained for the distribution of linear functions (e.g., predictors) of the post-model-selection estimator.

Keywords: Inference after model selection; Post-model-selection estimator; Pre-test estimator; Selection of regressors; Akaike's information criterion AIC; Thresholding; Model uncertainty; Consistency; Uniform consistency; Lower risk bound (search for similar items in EconPapers)
JEL-codes: C12 C13 C20 C51 C52 (search for similar items in EconPapers)
Date: 2005-04
New Economics Papers: this item is included in nep-ecm and nep-ets
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (13)

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https://mpra.ub.uni-muenchen.de/72/1/MPRA_paper_72.pdf original version (application/pdf)
https://mpra.ub.uni-muenchen.de/1895/1/MPRA_paper_1895.pdf revised version (application/pdf)

Related works:
Journal Article: CAN ONE ESTIMATE THE UNCONDITIONAL DISTRIBUTION OF POST-MODEL-SELECTION ESTIMATORS? (2008)
Working Paper: Can One Estimate the Conditional Distribution of Post-Model-Selection Estimators? (2003)
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Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:72

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