Empirical process results for exchangeable arrays

Laurent Davezies, Xavier D’haultfœuille and Yannick Guyonvarch
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Laurent Davezies: CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique
Xavier D’haultfœuille: CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique
Yannick Guyonvarch: Université Paris-Saclay

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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.

Keywords: exchangeable arrays empirical processes bootstrap; exchangeable arrays; empirical processes; bootstrap (search for similar items in EconPapers)
Date: 2021-04-01
Note: View the original document on HAL open archive server: https://hal.inrae.fr/hal-04430851v1
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Citations: View citations in EconPapers (8)

Published in Annals of Statistics, 2021, 49 (2), ⟨10.1214/20-AOS1981⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-04430851

DOI: 10.1214/20-AOS1981

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