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The Finite-Sample Distribution Of Post-Model-Selection Estimators And Uniform Versus Nonuniform Approximations

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  • Leeb, Hannes
  • Pötscher, Benedikt M.

Abstract

In Pötscher (1991, Econometric Theory 7, 163–185) the asymptotic distribution of a post-model-selection estimator, both unconditional and conditional on selecting a correct model (minimal or not), 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 with respect to the underlying parameters. In the present paper we first obtain the unconditional and also the conditional finite-sample distribution of the post-model-selection estimator, which turn 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 Pötscher (1991) but at the same time are close to the finite-sample distributions uniformly with respect to the underlying parameters. As a by-product, we also obtain the asymptotic distribution conditional on selecting an incorrect model.We thank the co-editor Richard Smith and the two referees for helpful comments on a previous version of this paper. Hannes Leeb's research was supported by the Austrian Science Foundation (FWF), project P13868-MAT.

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  • Leeb, Hannes & Pötscher, Benedikt M., 2003. "The Finite-Sample Distribution Of Post-Model-Selection Estimators And Uniform Versus Nonuniform Approximations," Econometric Theory, Cambridge University Press, vol. 19(1), pages 100-142, February.
  • Handle: RePEc:cup:etheor:v:19:y:2003:i:01:p:100-142_19
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    References listed on IDEAS

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

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