The Finite-Sample Distribution of Post-Model-Selection Estimators, and Uniform Versus Non-Uniform Approximations

Hannes Leeb () and Benedikt M. Poetscher
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Benedikt M. Poetscher: University of Vienna
Authors registered in the RePEc Author Service: Benedikt M Pötscher ()

Econometrics from EconWPA

Abstract: In 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.

Keywords: Model selection; post-model-selection estimator; pre-test estimator; asymptotic distribution; finite-sample distribution; uniform approximation (search for similar items in EconPapers)
JEL-codes: C20 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: 2000-04-03
Note: Type of Document - Postscript; prepared on IBM PC - Linux - LaTex; to print on PostScript; pages: 36 ; figures: none
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