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

Hannes Leeb and Benedikt M. P tscher

Econometric Theory, 2003, vol. 19, issue 01, pages 100-142

Abstract: In P tscher (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 P tscher (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.

Date: 2003
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