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

Hannes Leeb () and Benedikt Pötscher

No 1444, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: We consider the problem of estimating the conditional distribution of a post-model-selection estimator where the conditioning is on the selected model. 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 second 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 this 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 this distribution. Similar impossibility results are also obtained for the conditional 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; Akaikeis information criterion AIC; Model uncertainty; Consistency; Uniform consistency; Lower risk bound (search for similar items in EconPapers)
JEL-codes: C21 C50 (search for similar items in EconPapers)
Pages: 33 pages
Date: 2003-11
New Economics Papers: this item is included in nep-ecm and nep-ets
References: Add references at CitEc
Citations: View citations in EconPapers (23)

Published in Annals of Statistics (2006), 34: 2554-2591

Downloads: (external link)
https://cowles.yale.edu/sites/default/files/files/pub/d14/d1444.pdf (application/pdf)
Our link check indicates that this URL is bad, the error code is: 404 Not Found

Related works:
Journal Article: CAN ONE ESTIMATE THE UNCONDITIONAL DISTRIBUTION OF POST-MODEL-SELECTION ESTIMATORS? (2008)
Working Paper: Can One Estimate the Unconditional Distribution of Post-Model-Selection Estimators ? (2005)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:cwl:cwldpp:1444

Ordering information: This working paper can be ordered from
Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA
The price is None.

Access Statistics for this paper

More papers in Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University Yale University, Box 208281, New Haven, CT 06520-8281 USA. Contact information at EDIRC.
Bibliographic data for series maintained by Brittany Ladd ().