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ASYMPTOTIC SIZE AND A PROBLEM WITH SUBSAMPLING AND WITH THE m OUT OF n BOOTSTRAP

Published online by Cambridge University Press:  02 October 2009

Donald W.K. Andrews  and
Patrik Guggenberger
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Abstract

This paper considers inference based on a test statistic that has a limit distribution that is discontinuous in a parameter. The paper shows that subsampling and m out of n bootstrap tests based on such a test statistic often have asymptotic size—defined as the limit of exact size—that is greater than the nominal level of the tests. This is due to a lack of uniformity in the pointwise asymptotics. We determine precisely the asymptotic size of such tests under a general set of high-level conditions that are relatively easy to verify. The results show that the asymptotic size of subsampling and m out of n bootstrap tests is distorted in some examples but not in others.

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Type
Research Article
Information
Econometric Theory , Volume 26 , Issue 2 , April 2010 , pp. 426 - 468
Copyright
Copyright © Cambridge University Press 2009

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Footnotes

This paper previously circulated under the title “The Limit of Finite-Sample Size and a Problem with Subsampling” as Cowles Foundation Discussion Paper No. 1605. Andrews was supported by NSF grants SES-0417911 and SES-0751517. Guggenberger was supported by a Sloan fellowship, a UCLA faculty research grant in 2005 and NSF grant SES-0748922. For helpful comments, we thank two referees, the co-editor Richard Smith, Victor Chernozhukov, In Choi, Russell Davidson, Hannes Leeb, David Pollard, Azeem Shaikh, Jim Stock, Michael Wolf, and the participants at various seminars and conferences at which the paper was presented.

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