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The Bootstrap for Network Dependent Processes

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  • Denis Kojevnikov

Abstract

This paper focuses on the bootstrap for network dependent processes under the conditional $\psi$-weak dependence. Such processes are distinct from other forms of random fields studied in the statistics and econometrics literature so that the existing bootstrap methods cannot be applied directly. We propose a block-based approach and a modification of the dependent wild bootstrap for constructing confidence sets for the mean of a network dependent process. In addition, we establish the consistency of these methods for the smooth function model and provide the bootstrap alternatives to the network heteroskedasticity-autocorrelation consistent (HAC) variance estimator. We find that the modified dependent wild bootstrap and the corresponding variance estimator are consistent under weaker conditions relative to the block-based method, which makes the former approach preferable for practical implementation.

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  • Denis Kojevnikov, 2021. "The Bootstrap for Network Dependent Processes," Papers 2101.12312, arXiv.org.
    • Handle: RePEc:arx:papers:2101.12312
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    References listed on IDEAS

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    1. Kojevnikov, Denis & Marmer, Vadim & Song, Kyungchul, 2021. "Limit theorems for network dependent random variables," Journal of Econometrics, Elsevier, vol. 222(2), pages 882-908.
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    6. Kelejian, Harry H. & Prucha, Ingmar R., 2007. "HAC estimation in a spatial framework," Journal of Econometrics, Elsevier, vol. 140(1), pages 131-154, September.
    7. Shao, Xiaofeng, 2010. "The Dependent Wild Bootstrap," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 218-235.
    8. Calhoun, Gray, 2014. "Block Bootstrap Consistency Under Weak Assumptions," Staff General Research Papers Archive 34313, Iowa State University, Department of Economics.
    9. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2012. "Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors," Papers 1212.6906, arXiv.org, revised Jan 2018.
    10. Matyas,Laszlo (ed.), 1999. "Generalized Method of Moments Estimation," Cambridge Books, Cambridge University Press, number 9780521669672, January.
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    12. Conley, T. G., 1999. "GMM estimation with cross sectional dependence," Journal of Econometrics, Elsevier, vol. 92(1), pages 1-45, September.
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    Cited by:

    1. Timothy G. Conley & Sílvia Gonçalves & Min Seong Kim & Benoit Perron, 2023. "Bootstrap inference under cross‐sectional dependence," Quantitative Economics, Econometric Society, vol. 14(2), pages 511-569, May.
    2. Tadao Hoshino & Takahide Yanagi, 2021. "Causal Inference with Noncompliance and Unknown Interference," Papers 2108.07455, arXiv.org, revised Oct 2023.
    3. Michael P. Leung, 2022. "Causal Inference Under Approximate Neighborhood Interference," Econometrica, Econometric Society, vol. 90(1), pages 267-293, January.
    4. Michael P. Leung, 2023. "Network Cluster‐Robust Inference," Econometrica, Econometric Society, vol. 91(2), pages 641-667, March.
    5. Han Kevin & Ugander Johan, 2023. "Model-based regression adjustment with model-free covariates for network interference," Journal of Causal Inference, De Gruyter, vol. 11(1), pages 1-29, January.

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