Compound Poisson approximation of the number of exceedances in Gaussian sequences
type: Item
instance of: scholarly article
title: Compound Poisson approximation of the number of exceedances in Gaussian sequences
zbMATH Open document ID: 0929.60016
DOI: 10.1023/A:1009929800688
author: Mikael Raab
published in: Extremes
publication date: 1999-08-10T00:00:00Z
review text: For a finite stationary sequence of Gaussian random variables \(y_1,y_2,\dots,y_n\) with \(\rho_k=Ey_1y_{k+1}\), \(k=2,\dots,n-1\), define \(W\) as the number of variables exceeding some given level \(a\). When some \(\rho_k\) are positive and large, the author proposes to use the compound Poisson distribution which provides better rate of convergence for approximation of the true distribution of \(W\) than the ordinary Poisson distribution. Thus, a short review of the local version of the Stein approximation method for compound Poisson distribution is given and this general theory is applied to the problem of exceedances of \(m\)-dependent Gaussian sequences. The upper bounds for total variation distance between \(W\) and compound Poisson variable are obtained in the case of a finite sequence and any positive \(a\) as well as the asymptotic bounds in the case, when \(n\) and \(a\) increase, while \(EW\) is fixed. Approximation using only two-term compound Poisson distribution is discussed and results of numerical calculations and simulations are presented.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60G70
zbMATH DE Number: 1323314
zbMATH Keywords: compound Poisson approximation
zbMATH Keywords: Gaussian sequences
zbMATH Keywords: Stein-Chen method
zbMATH Keywords: extreme values
zbMATH Keywords: \(m\)-dependence
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1323314