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

Donald W.K. Andrews and Patrik Guggenberger

Journal of Econometrics, 2009, vol. 152, issue 1, pages 19-27

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.

Keywords: Asymptotic; size; Confidence; set; Finite-sample; size; m; out; of; n; bootstrap; Model; selection; Shrinkage; estimator; Subsample; Subsampling (search for similar items in EconPapers)
Date: 2009

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Persistent link: http://EconPapers.repec.org/RePEc:eee:econom:v:152:y:2009:i:1:p:19-27

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