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

Listed author(s):
  • Leeb, Hannes
  • P tscher, Benedikt M.

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.

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Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 19 (2003)
Issue (Month): 01 (February)
Pages: 100-142

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Handle: RePEc:cup:etheor:v:19:y:2003:i:01:p:100-142_19
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  1. 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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