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THE FINITE-SAMPLE DISTRIBUTION OF POST-MODEL-SELECTION ESTIMATORS AND UNIFORM VERSUS NONUNIFORM APPROXIMATIONS

Published online by Cambridge University Press:  08 January 2003

Hannes Leeb  and
Benedikt M. Pötscher
Hannes Leeb
Affiliation:
University of Vienna
Benedikt M. Pötscher
Affiliation:
University of Vienna
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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.

Type
Research Article
Information
Econometric Theory , Volume 19 , Issue 1 , February 2003 , pp. 100 - 142
Copyright
© 2003 Cambridge University Press

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References

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