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

Donald W.K. Andrews, Patrik Guggenberger

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

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 - α for any α ∈ (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.

Original languageEnglish (US)
Pages (from-to)19-27
Number of pages9
JournalJournal of Econometrics
Volume152
Issue number1
DOIs
StatePublished - Sep 1 2009

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics

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