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Empirical Process Results for Exchangeable Arrays

Author

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  • Laurent Davezies
  • Xavier D'Haultfoeuille
  • Yannick Guyonvarch

Abstract

Exchangeable arrays are natural tools to model common forms of dependence between units of a sample. Jointly exchangeable arrays are well suited to dyadic data, where observed random variables are indexed by two units from the same population. Examples include trade flows between countries or relationships in a network. Separately exchangeable arrays are well suited to multiway clustering, where units sharing the same cluster (e.g. geographical areas or sectors of activity when considering individual wages) may be dependent in an unrestricted way. We prove uniform laws of large numbers and central limit theorems for such exchangeable arrays. We obtain these results under the same moment restrictions and conditions on the class of functions as those typically assumed with i.i.d. data. We also show the convergence of bootstrap processes adapted to such arrays.

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  • Laurent Davezies & Xavier D'Haultfoeuille & Yannick Guyonvarch, 2019. "Empirical Process Results for Exchangeable Arrays," Papers 1906.11293, arXiv.org, revised May 2020.
    • Handle: RePEc:arx:papers:1906.11293
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    File URL: http://arxiv.org/pdf/1906.11293
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    References listed on IDEAS

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    1. Laurent Davezies & Xavier D'Haultfoeuille & Yannick Guyonvarch, 2018. "Asymptotic results under multiway clustering," Papers 1807.07925, arXiv.org, revised Aug 2018.
    2. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504.
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    Cited by:

    1. Harold D Chiang & Yukitoshi Matsushita & Taisuke Otsu, 2021. "Multiway empirical likelihood," Papers 2108.04852, arXiv.org, revised Dec 2023.
    2. MacKinnon, James G. & Nielsen, Morten Ørregaard & Webb, Matthew D., 2023. "Cluster-robust inference: A guide to empirical practice," Journal of Econometrics, Elsevier, vol. 232(2), pages 272-299.
    3. Bryan S. Graham, 2019. "Network Data," Papers 1912.06346, arXiv.org.
    4. Bryan S. Graham, 2019. "Dyadic Regression," Papers 1908.09029, arXiv.org.
    5. Harold D Chiang & Yukun Ma & Joel Rodrigue & Yuya Sasaki, 2021. "Dyadic double/debiased machine learning for analyzing determinants of free trade agreements," Papers 2110.04365, arXiv.org, revised Dec 2022.
    6. Bryan S. Graham, 2019. "Network Data," CeMMAP working papers CWP71/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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