Remarks on compound Poisson approximation of Gaussian random sequences

Détails

ID Serval
serval:BIB_EBE1C955F286
Type
Article: article d'un périodique ou d'un magazine.
Collection
Publications
Titre
Remarks on compound Poisson approximation of Gaussian random sequences
Périodique
Statistics & Probability Letters
Auteur⸱e⸱s
Hashorva E., Huesler J.
ISSN
0167-7152
Statut éditorial
Publié
Date de publication
2002
Peer-reviewed
Oui
Volume
57
Numéro
1
Pages
1-8
Langue
anglais
Résumé
Let {X-i, i greater than or equal to 1} be a sequence of m-dependent stationary standard Gaussian random variables and u(n), n is an element of N some positive constants. In this note we generalise results of Raab (Extremes 1(3) (1999) 29.), who considered compound Poisson approximation for W-n = Sigma(i=1)(n) 1{X-i > u(n)} the number of exceedances above the level u(n). More precisely, the main result concerns an upper asymptotic bound for the total variational distance d(TV)(W-n,CP(lambda*)) where CP(lambda*) =(d) N-1 + 2N(2) +...+ rN(r), with 2 less than or equal to r less than or equal to 2m and N-i =(d) Poi(lambda(i)), lambda(i) > 0 are independent Poisson random variables.
Mots-clé
Rate of convergence, Compound Poisson approximation, Stein-Chen method, Extreme values, Stationary Gaussian sequences, Quadratic programming
Web of science
Création de la notice
03/09/2010 12:24
Dernière modification de la notice
20/08/2019 17:14
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