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Incorrect asymptotic size of subsampling procedures based on post-consistent model selection estimators

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  • Andrews, Donald W.K.
  • Guggenberger, Patrik

Abstract

Subsampling and the m out of n bootstrap have been suggested in the literature as methods for carrying out inference based on post-model selection estimators and shrinkage estimators. In this paper we consider a subsampling confidence interval (CI) that is based on an estimator that can be viewed either as a post-model selection estimator that employs a consistent model selection procedure or as a super-efficient estimator. We show that the subsampling CI (of nominal level 1-[alpha] for any [alpha][set membership, variant](0,1)) has asymptotic confidence size (defined to be the limit of finite-sample size) equal to zero in a very simple regular model. The same result holds for the m out of n bootstrap provided m2/n-->0 and the observations are i.i.d. Similar zero-asymptotic-confidence-size results hold in more complicated models that are covered by the general results given in the paper and for super-efficient and shrinkage estimators that are not post-model selection estimators. Based on these results, subsampling and the m out of n bootstrap are not recommended for obtaining inference based on post-consistent model selection or shrinkage estimators.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 152 (2009)
Issue (Month): 1 (September)
Pages: 19-27

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Handle: RePEc:eee:econom:v:152:y:2009:i:1:p:19-27

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Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Asymptotic size Confidence set Finite-sample size m out of n bootstrap Model selection Shrinkage estimator Subsample Subsampling;

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Cited by:
  1. Camponovo, Lorenzo & Scaillet, Olivier & Trojani, Fabio, 2012. "Robust subsampling," Journal of Econometrics, Elsevier, vol. 167(1), pages 197-210.
  2. Adam McCloskey, 2012. "Bonferroni-Based Size-Correction for Nonstandard Testing Problems," Working Papers 2012-16, Brown University, Department of Economics.
  3. Donald W.K. Andrews & Patrik Guggenberger, 2007. "Applications of Subsampling, Hybrid, and Size-Correction Methods," Cowles Foundation Discussion Papers 1608, Cowles Foundation for Research in Economics, Yale University.
  4. Donald W.K. Andrews & Xu Cheng & Patrik Guggenberger, 2011. "Generic Results for Establishing the Asymptotic Size of Confidence Sets and Tests," Cowles Foundation Discussion Papers 1813, Cowles Foundation for Research in Economics, Yale University.
  5. Guggenberger, Patrik, 2010. "The impact of a Hausman pretest on the size of a hypothesis test: The panel data case," Journal of Econometrics, Elsevier, vol. 156(2), pages 337-343, June.

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