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The Continuity Of The Limit Distribution In The Parameter Of Interest Is Not Essential For The Validity Of The Bootstrap

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  • Inoue, Atsushi
  • Kilian, Lutz

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.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 19 (2003)
Issue (Month): 06 (December)
Pages: 944-961

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Handle: RePEc:cup:etheor:v:19:y:2003:i:06:p:944-961_19

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Cited by:
  1. DUFOUR, Jean-Marie, 2005. "Monte Carlo Tests with Nuisance Parameters: A General Approach to Finite-Sample Inference and Nonstandard Asymptotics," Cahiers de recherche 2005-03, Universite de Montreal, Departement de sciences economiques.
  2. DUFOUR, Jean-Marie & JOUINI, Tarek, 2005. "Finite-Sample Simulation-Based Inference in VAR Models with Applications to Order Selection and Causality Testing," Cahiers de recherche 16-2005, Centre interuniversitaire de recherche en ├ęconomie quantitative, CIREQ.
  3. Dufour, Jean-Marie & Jouini, Tarek, 2006. "Finite-sample simulation-based inference in VAR models with application to Granger causality testing," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 229-254.
  4. Kilian, Lutz & Kim, Yun Jung, 2009. "Do Local Projections Solve the Bias Problem in Impulse Response Inference?," CEPR Discussion Papers 7266, C.E.P.R. Discussion Papers.

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