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VALIDITY OF SUBSAMPLING AND “PLUG-IN ASYMPTOTIC” INFERENCE FOR PARAMETERS DEFINED BY MOMENT INEQUALITIES

Published online by Cambridge University Press:  01 June 2009

Donald W.K. Andrews  and
Patrik Guggenberger
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Abstract

This paper considers inference for parameters defined by moment inequalities and equalities. The parameters need not be identified. For a specified class of test statistics, this paper establishes the uniform asymptotic validity of subsampling, m out of n bootstrap, and “plug-in asymptotic” tests and confidence intervals for such parameters. Establishing uniform asymptotic validity is crucial in moment inequality problems because the pointwise asymptotic distributions of the test statistics of interest have discontinuities as functions of the true distribution that generates the observations.

The size results are quite general because they hold without specifying the particular form of the moment conditions—only 2 + δ moments finite are required. The results allow for independent and identically distributed (i.i.d.) and dependent observations and for preliminary consistent estimation of identified parameters.

Type
Research Article
Information
Econometric Theory , Volume 25 , Issue 3 , June 2009 , pp. 669 - 709
Copyright
Copyright © Cambridge University Press 2009

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Footnotes

Andrews gratefully acknowledges the research support of the National Science Foundation via grant SES-0417911. Guggenberger gratefully acknowledges research support from a faculty research grant from UCLA in 2005 and from the National Science Foundation via grant SES-0748922. For helpful comments, we thank two referees, the co-editor Richard Smith, Ivan Canay, Victor Chernozukhov, Azeem Shaikh, and the participants at various seminars and conferences at which the paper was presented. Some of the results in this paper first appeared in D.W.K. Andrews and P. Guggenberger (2005), “The Limit of Finite-Sample Size and a Problem with Subsampling,” Cowles Foundation Discussion paper 1606, Yale University.

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