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Domains of attraction of the real random vector (X,X²) and applications

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  • Omey, Edward

    ()
    (Hogeschool-Universiteit Brussel (HUB), Belgium)

  • Van Gulck, Stefan

    ()
    (Hogeschool-Universiteit Brussel (HUB), Belgium)

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    Abstract

    Many statistics are based on functions of sample moments. Important examples are the sample variance s2(n), the sample coefficient of variation SV (n), the sample dispersion SD(n) and the non-central t-statistic t(n). The de.nition of these quantities makes clear that the vector defined by XXX plays an important role. In the paper we obtain conditions under which the vector (X;X2) belongs to a bivariate domain of attraction of a stable law. Applying simple transformations then leads to a full discussion of the asymptotic behaviour of SV (n) and t(n).

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    File URL: http://lirias.hubrussel.be/handle/123456789/2219
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    Bibliographic Info

    Paper provided by Hogeschool-Universiteit Brussel, Faculteit Economie en Management in its series Working Papers with number 2008/02.

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    Length: 17 pages
    Date of creation: Jan 2008
    Date of revision:
    Handle: RePEc:hub:wpecon:200802

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    Web page: http://research.hubrussel.be
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