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

Atsushi Inoue and Lutz Kilian

Econometric Theory, 2003, vol. 19, issue 6, 944-961

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.

Date: 2003
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