The Finite-Sample Distribution of Post-Model-Selection Estimators, and Uniform Versus Non-Uniform Approximations
AbstractIn Poetscher [Econometric Theory (1991), 7, pp 163 - 185] the asymptotic distribution of a post-model-selection estimator, both unconditional and conditional on selecting a correct model, has been derived. Limitations of these results are (i) that they do not provide information on the distribution of the post-model-selection estimator conditional on selecting an incorrect model, and (ii) that the quality of this asymptotic approximation to the finite-sample distribution is not uniform w.r.t. the underlying parameters. In the present paper we first obtain the unconditional as well as the conditional finite-sample distribution of the post-model-selection estimator which turns out to be complicated and difficult to interpret. Second, we obtain approximations to the finite-sample distributions that are as simple and easy to interpret as the asymptotic distributions obtained in Poetscher [Econometric Theory (1991), 7, pp 163 - 185], but at the same time are close to the finite-sample distributions uniformly w.r.t. the underlying parameters. As a by-product, we also obtain the asymptotic distribution conditional on selecting an incorrect model.
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Bibliographic InfoPaper provided by EconWPA in its series Econometrics with number 0004001.
Length: 36 pages
Date of creation: 03 Apr 2000
Date of revision:
Note: Type of Document - Postscript; prepared on IBM PC - Linux - LaTex; to print on PostScript; pages: 36 ; figures: none
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Model selection; post-model-selection estimator; pre-test estimator; asymptotic distribution; finite-sample distribution; uniform approximation;
Other versions of this item:
- Leeb, Hannes & P tscher, Benedikt M., 2003. "The Finite-Sample Distribution Of Post-Model-Selection Estimators And Uniform Versus Nonuniform Approximations," Econometric Theory, Cambridge University Press, vol. 19(01), pages 100-142, February.
- C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
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- Pötscher, B.M., 1991. "Effects of Model Selection on Inference," Econometric Theory, Cambridge University Press, vol. 7(02), pages 163-185, June.
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