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Empirical process results for exchangeable arrays

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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 - 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 - CNRS - Centre National de la Recherche Scientifique)

  • Yannick Guyonvarch

    (Université Paris-Saclay)

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.

Suggested Citation

  • Laurent Davezies & Xavier D’haultfœuille & Yannick Guyonvarch, 2021. "Empirical process results for exchangeable arrays," Post-Print hal-04430851, HAL.
    • Handle: RePEc:hal:journl:hal-04430851
    DOI: 10.1214/20-AOS1981
    Note: View the original document on HAL open archive server: https://hal.inrae.fr/hal-04430851
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    References listed on IDEAS

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    1. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, September.
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    Cited by:

    1. Diegert, Paul & Jochmans, Koen, 2024. "Nonparametric Identification of Models for Dyadic Data”," TSE Working Papers 24-1574, Toulouse School of Economics (TSE).
    2. Nan Liu & Yanbo Liu & Yuya Sasaki, 2024. "Estimation and Inference for Causal Functions with Multiway Clustered Data," Papers 2409.06654, arXiv.org.
    3. James G. MacKinnon & Morten {O}rregaard Nielsen & Matthew D. Webb, 2024. "Jackknife inference with two-way clustering," Papers 2406.08880, arXiv.org.
    4. Richard K. Crump & Nikolay Gospodinov & Ignacio Lopez Gaffney, 2024. "A Jackknife Variance Estimator for Panel Regressions," Staff Reports 1133, Federal Reserve Bank of New York.

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