Remarks on compound Poisson approximation of Gaussian random sequences

Details

Serval ID
serval:BIB_EBE1C955F286
Type
Article: article from journal or magazin.
Collection
Publications
Title
Remarks on compound Poisson approximation of Gaussian random sequences
Journal
Statistics & Probability Letters
Author(s)
Hashorva E., Huesler J.
ISSN
0167-7152
Publication state
Published
Issued date
2002
Peer-reviewed
Oui
Volume
57
Number
1
Pages
1-8
Language
english
Abstract
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.
Keywords
Rate of convergence, Compound Poisson approximation, Stein-Chen method, Extreme values, Stationary Gaussian sequences, Quadratic programming
Web of science
Create date
03/09/2010 11:24
Last modification date
20/08/2019 16:14
Usage data