Generalized quantile processes

J.H.J. Einmahl, D.M. Mason

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    Abstract

    For random vectors taking values in $\mathbb{R}^d$ we introduce a notion of multivariate quantiles defined in terms of a class of sets and study an associated process which we call the generalized quantile process. This process specializes to the well known univariate quantile process. We obtain functional central limit theorems for our generalized quantile process and show that both Gaussian and non-Gaussian limiting processes can arise. A number of interesting example are included.
    Original languageEnglish
    Pages (from-to)1062-1078
    Number of pages17
    JournalThe Annals of Statistics
    Volume20
    Issue number2
    DOIs
    Publication statusPublished - 1992

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