Max-semistable hemigroups : structure, domains of attrac

• Autorzy: Becker-Kern, P.
• Języki publikacji: EN

Abstrakty

EN

Let (X_n) be a sequence of independent real valued random variables. A suitable convergence condition for affine normalized maxima of (X_n) is given in the semistable setup, i.e. for increasing sampling sequences (k_n) such that k_n+1/k_n→c >1, which enables us to obtain a hemigroup structure in the limit. We show that such hemigroups are closely related to max-semi self decomposable laws and that the norming sequences of the convergence condition can be chosen such that the limiting behaviour for arbitrary sampling sequences can be fully analysed. Thisin turn enables us to obtain randomized limits as follows. Suppose that (T_n) is a sequence of positive integer valued random variables such that T_n/k_nor T_n/n convergesin probability to some positive random variable D, where we do not assume (X_n) and (T_n) to be independent. Then weak limit theorems of randomized extremes, where the sampling sequence (k_n) is replaced by random sample sizes (T_n), are presented. The proof follows corresponding results on the central limit theorem, containing the verification of an Anscombe condition.

Słowa kluczowe

EN

extreme values; max-semistable distributions; hemigroup; max-semi self decomposability; random sample size; randomized limit theorem; Anscombe condition

• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2001
• Tom: Vol. 21, Fasc. 2
• Strony: 441--465
• Opis fizyczny: Bibliogr.17 poz.

Twórcy

autor

Becker-Kern, P.

• Fachbereich Mathematik, Universität Dortmund, 44221 Dortmund, Germany,

Bibliografia

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