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ASYMPTOTIC SIZE AND A PROBLEM WITHSUBSAMPLING AND WITH THE m OUT OFn BOOTSTRAP

Published online by Cambridge University Press:  02 October 2009

Donald W.K. Andrews and
Patrik Guggenberger
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Abstract

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This paper considers inference based on a teststatistic that has a limit distribution that isdiscontinuous in a parameter. The paper shows thatsubsampling and m out ofn bootstrap tests based on such atest statistic often have asymptotic size—defined asthe limit of exact size—that is greater than thenominal level of the tests. This is due to a lack ofuniformity in the pointwise asymptotics. Wedetermine precisely the asymptotic size of suchtests under a general set of high-level conditionsthat are relatively easy to verify. The results showthat the asymptotic size of subsampling andm out of nbootstrap tests is distorted in some examples butnot in others.

Information

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

Footnotes

This paper previously circulated under the title“The Limit of Finite-Sample Size and a Problemwith Subsampling” as Cowles Foundation DiscussionPaper No. 1605. Andrews was supported by NSFgrants SES-0417911 and SES-0751517. Guggenbergerwas supported by a Sloan fellowship, a UCLAfaculty research grant in 2005 and NSF grantSES-0748922. For helpful comments, we thank tworeferees, the co-editor Richard Smith, VictorChernozhukov, In Choi, Russell Davidson, HannesLeeb, David Pollard, Azeem Shaikh, Jim Stock,Michael Wolf, and the participants at variousseminars and conferences at which the paper waspresented.

References

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