The asymptotics of L-statistics for non i.i.d. variables with heavy tails

• Autorzy: Barczyk A. , Janssen A. , Pauly M.
• Języki publikacji: EN

Abstrakty

EN

The purpose of this paper is to study the asymptotic behaviour of linear combinations of order statistics (L-statistics)... [formula] for variables with heavy tails. The order statisticsXi:kn correspond to a non i.i.d. triangular array (X_i,n)1≤i≤k_n of infinitesimal and rowwise independent random variables. We give sufficient conditions for the convergence of L-statistics to non-normal limit laws and it is shown that only the extremes contribute to the limit distribution, whereas the middle parts vanish. As an example we consider the case, where the extremal partial sums belong to the domain of attraction of a stable law.We also study L-statistics with scores defined by c_i,n := J(i/(n + 1)) with a regularly varying function J, a case which has often been treated in the literature.

Słowa kluczowe

EN

L-statistics; shift-compactness; order statistics; heavy tails; stable law; non i.i.d. array

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2011
• Tom: Vol. 31, Fasc. 2
• Strony: 285--299
• Opis fizyczny: Bibliogr. 29 poz.

Twórcy

autor

Barczyk A.

• Mathematisches Institut, der Heinrich-Heine Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany

autor

Janssen A.

• Mathematisches Institut, der Heinrich-Heine Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany

autor

Pauly M.

• Mathematisches Institut, der Heinrich-Heine Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany

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