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Block Bootstrap Consistency Under Weak Assumptions

  • Calhoun, Gray

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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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: 06 Oct 2014
Date of revision:
Handle: RePEc:isu:genres:34313
Contact details of provider: Postal: Iowa State University, Dept. of Economics, 260 Heady Hall, Ames, IA 50011-1070
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  1. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
  2. de Jong, Robert M. & Davidson, James, 2000. "The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals I," Econometric Theory, Cambridge University Press, vol. 16(05), pages 621-642, October.
  3. Sílvia Gonçalves & Halbert White, 2001. "The Bootstrap of the Mean for Dependent Heterogeneous Arrays," CIRANO Working Papers 2001s-19, CIRANO.
  4. 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.
  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. 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.
  7. 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.
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