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THE CONTINUITY OF THE LIMIT DISTRIBUTION IN THE PARAMETER OF INTEREST IS NOT ESSENTIAL FOR THE VALIDITY OF THE BOOTSTRAP

Published online by Cambridge University Press:  24 September 2003

Atsushi Inoue  and
Lutz Kilian
Atsushi Inoue
Affiliation:
North Carolina State University
Lutz Kilian
Affiliation:
University of Michigan, European Central Bank, and CEPR
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Abstract

It is well known that the unrestricted bootstrap estimator of the slope parameter in the random walk model without drift converges to a random distribution. This bootstrap failure is commonly attributed to the discontinuity of the limit distribution of the least-squares estimator in the parameter of interest. We demonstrate by counterexample that this type of continuity is not essential for the validity of the bootstrap nor is it essential that the rate of convergence of the estimator remain constant over the whole parameter space.We thank Don Andrews, Shinichi Sakata, Jonathan Wright, and two anonymous referees for very helpful comments. The views expressed in this paper do not necessarily reflect those of the European Central Bank or its members.

Type
Research Article
Information
Econometric Theory , Volume 19 , Issue 6 , December 2003 , pp. 944 - 961
Copyright
© 2003 Cambridge University Press

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