April 2021 Empirical process results for exchangeable arrays
Laurent Davezies, Xavier D’Haultfœuille, Yannick Guyonvarch
Author Affiliations +
Ann. Statist. 49(2): 845-862 (April 2021). DOI: 10.1214/20-AOS1981


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’Haultfœuille. Yannick Guyonvarch. "Empirical process results for exchangeable arrays." Ann. Statist. 49 (2) 845 - 862, April 2021. https://doi.org/10.1214/20-AOS1981


Received: 1 April 2020; Revised: 1 May 2020; Published: April 2021
First available in Project Euclid: 2 April 2021

Digital Object Identifier: 10.1214/20-AOS1981

Primary: 60F17
Secondary: 60G09 , 62F40

Keywords: bootstrap , Empirical processes , Exchangeable arrays

Rights: Copyright © 2021 Institute of Mathematical Statistics


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Vol.49 • No. 2 • April 2021
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