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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 (NED) functions of mixing processes; they are consistent under the weakest conditions that ensure the original NED process obeys a central limit theorem (CLT), established by De Jong (1997, Econometric Theory 13(3), 353–367). 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 (FCLT) under the same conditions.

Suggested Citation

  • Calhoun, Gray, 2018. "Block Bootstrap Consistency Under Weak Assumptions," Econometric Theory, Cambridge University Press, vol. 34(6), pages 1383-1406, December.
    • Handle: RePEc:cup:etheor:v:34:y:2018:i:06:p:1383-1406_00
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    Cited by:

    1. Lee, Sangyeol & Meintanis, Simos G. & Pretorius, Charl, 2022. "Monitoring procedures for strict stationarity based on the multivariate characteristic function," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    2. Lazar, Emese & Wang, Shixuan & Xue, Xiaohan, 2023. "Loss function-based change point detection in risk measures," European Journal of Operational Research, Elsevier, vol. 310(1), pages 415-431.
    3. Denis Kojevnikov, 2021. "The Bootstrap for Network Dependent Processes," Papers 2101.12312, arXiv.org.

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