Poisson and Gaussian approximation of weighted local empirical processes

J.H.J. Einmahl

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    Abstract

    We consider the local empirical process indexed by sets, a greatly generalized version of the well-studied uniform tail empirical process. We show that the weak limit of weighted versions of this process is Poisson under certain conditions, whereas it is Gaussian in other situations. Our main theorems provide a unified approach to a number of asymptotic distributional results for weighted empirical processes, which up to now appeared to be isolated facts. Our results are likely to have applications in local statistical procedures, e.g., in the study of multivariate extreme values.
    Original languageEnglish
    Place of PublicationEindhoven
    PublisherTechnische Universiteit Eindhoven
    Number of pages29
    Publication statusPublished - 1995

    Publication series

    NameMemorandum COSOR
    Volume9530
    ISSN (Print)0926-4493

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