Block Bootstrap Consistency Under Weak Assumptions
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.
|Date of creation:||06 Oct 2014|
|Date of revision:|
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- Davidson, James & de Jong, Robert M., 2000.
"The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals Ii,"
Cambridge University Press, vol. 16(05), pages 643-666, October.
- 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.
- 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.
- Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037, December.
- 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.
- Gon alves, S lvia & White, Halbert, 2002.
"The Bootstrap Of The Mean For Dependent Heterogeneous Arrays,"
Cambridge University Press, vol. 18(06), pages 1367-1384, December.
- Sílvia Gonçalves & Halbert White, 2001. "The Bootstrap of the Mean for Dependent Heterogeneous Arrays," CIRANO Working Papers 2001s-19, CIRANO.
- 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.
- 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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