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

Donald W K Andrews, Patrik Guggenberger

Research output: Contribution to journalArticle

16 Citations (Scopus)

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

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Subsampling
Model Selection
Shrinkage Estimator
Estimator
Bootstrap
Efficient Estimator
Confidence
Confidence interval
Selection Procedures
Zero
Categorical or nominal
Sample Size
Model selection
Model
Shrinkage estimator
Shrinkage

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics
  • Applied Mathematics
  • History and Philosophy of Science

Cite this

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Incorrect asymptotic size of subsampling procedures based on post-consistent model selection estimators. / Andrews, Donald W K; Guggenberger, Patrik.

In: Journal of Econometrics, Vol. 152, No. 1, 01.09.2009, p. 19-27.

Research output: Contribution to journalArticle

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