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The Marcinkiewicz–Zygmund law of large numbers 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] - GENES - Groupe des Écoles Nationales d'Économie et Statistique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - GENES - Groupe des Écoles Nationales d'Économie et Statistique - 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] - GENES - Groupe des Écoles Nationales d'Économie et Statistique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - GENES - Groupe des Écoles Nationales d'Économie et Statistique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

  • Yannick Guyonvarch

    (UMR PSAE - Paris-Saclay Applied Economics - AgroParisTech - Université Paris-Saclay - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

Abstract

We show a Marcinkiewicz-Zygmund law of large numbers for jointly, dissociated exchangeable arrays, in L r (r ∈ (0, 2)) and almost surely. Then, we obtain a law of iterated logarithm for such arrays under a weaker moment condition than the existing one.

Suggested Citation

  • Laurent Davezies & Xavier D’haultfœuille & Yannick Guyonvarch, 2022. "The Marcinkiewicz–Zygmund law of large numbers for exchangeable arrays," Post-Print hal-04430986, HAL.
    • Handle: RePEc:hal:journl:hal-04430986
    DOI: 10.1016/j.spl.2022.109536
    Note: View the original document on HAL open archive server: https://hal.inrae.fr/hal-04430986v1
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