Leeb, Hannes and Pötscher, Benedikt M. (2005): Can One Estimate the Unconditional Distribution of PostModelSelection Estimators ?
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Abstract
We consider the problem of estimating the unconditional distribution of a postmodelselection estimator. The notion of a postmodelselection 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 leastsquares 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 postmodelselection estimator.
Item Type:  MPRA Paper 

Original Title:  Can One Estimate the Unconditional Distribution of PostModelSelection Estimators ? 
Language:  English 
Keywords:  Inference after model selection; Postmodelselection estimator; Pretest estimator; Selection of regressors; Akaike's information criterion AIC; Thresholding; Model uncertainty; Consistency; Uniform consistency; Lower risk bound 
Subjects:  C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C20  General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C52  Model Evaluation, Validation, and Selection C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C12  Hypothesis Testing: General C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C51  Model Construction and Estimation 
Item ID:  72 
Depositing User:  Benedikt Poetscher 
Date Deposited:  12 Oct 2006 
Last Modified:  08 Oct 2016 19:37 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/72 
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