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

Author

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  • Hannes Leeb

    (University of Vienna)

  • Benedikt M. Poetscher

    (University of Vienna)

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.

Suggested Citation

  • Hannes Leeb & Benedikt M. Poetscher, 2000. "The Finite-Sample Distribution of Post-Model-Selection Estimators, and Uniform Versus Non-Uniform Approximations," Econometrics 0004001, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpem:0004001
    Note: Type of Document - Postscript; prepared on IBM PC - Linux - LaTex; to print on PostScript; pages: 36 ; figures: none
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    References listed on IDEAS

    as
    1. Pötscher, B.M., 1991. "Effects of Model Selection on Inference," Econometric Theory, Cambridge University Press, vol. 7(2), pages 163-185, June.
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    More about this item

    Keywords

    Model selection; post-model-selection estimator; pre-test estimator; asymptotic distribution; finite-sample distribution; uniform approximation;
    All these keywords.

    JEL classification:

    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General

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