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Block Bootstrap Consistency Under Weak Assumptions

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  • Calhoun, Gray

Abstract

This paper weakens the size and moment conditions needed for typical block bootstrap methods (i.e. the moving blocks, circular blocks, and stationary bootstraps) to be valid for the sample mean of Near-Epoch-Dependent functions of mixing processes; they are consistent under the weakest conditions that ensure the original process obeys a Central Limit Theorem (those of de Jong, 1997, Econometric Theory).� In doing so, this paper extends de Jong's method of proof, a blocking argument, to hold with random and unequal block lengths.� This paper also proves that bootstrapped partial sums satisfy a Functional CLT under the same conditions.

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File URL: http://www.econ.iastate.edu/sites/default/files/publications/papers/p14313-2011-09-23.pdf
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Paper provided by Iowa State University, Department of Economics in its series Staff General Research Papers with number 34313.

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Date of creation: 25 Mar 2013
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Handle: RePEc:isu:genres:34313

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Postal: Iowa State University, Dept. of Economics, 260 Heady Hall, Ames, IA 50011-1070
Phone: +1 515.294.6741
Fax: +1 515.294.0221
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Web page: http://www.econ.iastate.edu
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Keywords: Resampling; Time Series; Near Epoch Dependence; Functional Central Limit Theorem;

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  1. Gon alves, S lvia & White, Halbert, 2002. "The Bootstrap Of The Mean For Dependent Heterogeneous Arrays," Econometric Theory, Cambridge University Press, vol. 18(06), pages 1367-1384, December.
  2. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037, October.
  3. Goncalves, Silvia & de Jong, Robert, 2003. "Consistency of the stationary bootstrap under weak moment conditions," Economics Letters, Elsevier, vol. 81(2), pages 273-278, November.
  4. Davidson, James, 1992. "A Central Limit Theorem for Globally Nonstationary Near-Epoch Dependent Functions of Mixing Processes," Econometric Theory, Cambridge University Press, vol. 8(03), pages 313-329, September.
  5. de Jong, Robert M., 1997. "Central Limit Theorems for Dependent Heterogeneous Random Variables," Econometric Theory, Cambridge University Press, vol. 13(03), pages 353-367, June.
  6. Davidson, James & de Jong, Robert M., 2000. "The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals Ii," Econometric Theory, Cambridge University Press, vol. 16(05), pages 643-666, October.
  7. Davidson, James, 1993. "An L1-convergence theorem for heterogeneous mixingale arrays with trending moments," Statistics & Probability Letters, Elsevier, vol. 16(4), pages 301-304, March.
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