The Limit of Finite-Sample Size and a Problem with Subsampling

Donald W. K. Andrews () and Patrik Guggenberger
Additional contact information
Patrik Guggenberger: Dept. of Economics, UCLA

No 1605, Cowles Foundation Discussion Papers from Cowles Foundation, Yale University

Abstract: This paper considers inference based on a test statistic that has a limit distribution that is discontinuous in a nuisance parameter or the parameter of interest. The paper shows that subsample, b_n < n bootstrap, and standard fixed critical value tests based on such a test statistic often have asymptotic size -- defined as the limit of the finite-sample size -- that is greater than the nominal level of the tests. We determine precisely the asymptotic size of such tests under a general set of high-level conditions that are relatively easy to verify. The high-level conditions are verified in several examples. Analogous results are established for confidence intervals. The results apply to tests and confidence intervals (i) when a parameter may be near a boundary, (ii) for parameters defined by moment inequalities, (iii) based on super-efficient or shrinkage estimators, (iv) based on post-model selection estimators, (v) in scalar and vector autoregressive models with roots that may be close to unity, (vi) in models with lack of identification at some point(s) in the parameter space, such as models with weak instruments and threshold autoregressive models, (vii) in predictive regression models with nearly-integrated regressors, (viii) for non-differentiable functions of parameters, and (ix) for differentiable functions of parameters that have zero first-order derivative. Examples (i)-(iii) are treated in this paper. Examples (i) and (iv)-(vi) are treated in sequels to this paper, Andrews and Guggenberger (2005a, b). In models with unidentified parameters that are bounded by moment inequalities, i.e., example (ii), certain subsample confidence regions are shown to have asymptotic size equal to their nominal level. In all other examples listed above, some types of subsample procedures do not have asymptotic size equal to their nominal level.

Keywords: Asymptotic size; b < n bootstrap; Finite-sample size; Over-rejection; Size correction; Subsample confidence interval; Subsample test (search for similar items in EconPapers)
JEL-codes: C12 C15 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: 2007-03
View list of references View citations in EconPapers

Downloads: (external link)
http://cowles.econ.yale.edu/P/cd/d16a/d1605.pdf (application/pdf)

Related works:
Working Paper: The Limit of Finite-Sample Size and a Problem with Subsampling (2007)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: http://EconPapers.repec.org/RePEc:cwl:cwldpp:1605

Ordering information: This working paper can be ordered from
Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA
The price is None.

Access Statistics for this paper

More papers in Cowles Foundation Discussion Papers from Cowles Foundation, Yale University
Address: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Contact information at EDIRC.
Series data maintained by Glena Ames ().