Poisson and Gaussian approximation of weighted local empirical processes

J.H.J. Einmahl

    Research output: Contribution to journalArticleAcademicpeer-review

    28 Citations (Scopus)

    Abstract

    We consider the local empirical process indexed by sets, a substantial generalization 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 many new results as well as 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 have applications in ‘local’ statistical procedures; we will, in particular, show their usefulness in multivariate extreme value theory.
    Original languageEnglish
    Pages (from-to)31-58
    JournalStochastic Processes and their Applications
    Volume70
    Issue number1
    DOIs
    Publication statusPublished - 1997

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