JSM 2004 - Toronto

Abstract #300032

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Activity Number: 175
Type: Invited
Date/Time: Tuesday, August 10, 2004 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistical Computing
Abstract - #300032
Title: Can One Estimate the Distribution of Post-model-selection Estimators?
Author(s): Benedikt M. Pötscher*+ and Hannes Leeb
Companies: University of Vienna and Yale University
Address: Universitaetsstrasse 5, Vienna, International, A-1010, Austria
Keywords: inference ; model selection ; model uncertainty ; AIC ; uniform consistency
Abstract:

We consider the problem of estimating the 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 second, estimating the parameters in the selected model (e.g., by least-squares or maximum likelihood), all based on the same dataset. 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 distribution of linear functions (e.g., predictors) of the post-model-selection estimator.

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