Can One Estimate the Conditional Distribution of Post-Model-Selection Estimators?
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.
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| Length: | 33 pages |
| Date of creation: | Nov 2003 |
| Publication status: | Published in Annals of Statistics (2006), 34: 2554-2591 |
| Handle: | RePEc:cwl:cwldpp:1444 |
| Contact details of provider: | Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA Phone: (203) 432-3702 Fax: (203) 432-6167 Web page: http://cowles.yale.edu/ More information through EDIRC
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| Order Information: | Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA |
References listed on IDEAS
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"Can One Estimate The Unconditional Distribution Of Post-Model-Selection Estimators?,"
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- Hannes Leeb & Benedikt M. Potscher, 2003. "Can One Estimate the Conditional Distribution of Post-Model-Selection Estimators?," Cowles Foundation Discussion Papers 1444, Cowles Foundation for Research in Economics, Yale University.
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- Kabaila, Paul, 1995. "The Effect of Model Selection on Confidence Regions and Prediction Regions," Econometric Theory, Cambridge University Press, vol. 11(03), pages 537-549, June.
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- Danilov, Dmitry & Magnus, J.R.Jan R., 2004. "On the harm that ignoring pretesting can cause," Journal of Econometrics, Elsevier, vol. 122(1), pages 27-46, September. Full references (including those not matched with items on IDEAS)
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