Asymptotic \((r-1)\)-dependent representation for \(r\)th order statistic from a stationary sequence
type: Item
instance of: scholarly article
title: Asymptotic \((r-1)\)-dependent representation for \(r\)th order statistic from a stationary sequence
zbMATH Open document ID: 0773.60024
DOI: 10.1016/0304-4149(93)90084-H
author: Adam Jakubowski
published in: Stochastic Processes and their Applications
publication date: 1993-07-21T00:00:00Z
review text: Let \(X_ 1,\dots,X_ n\) be a stationary sequence. Its \(k\)th largest value is denoted by \(M_ n^{(k)}\). The author derives conditions for the existence of an \((r-1)\)-dependent stationary sequence \(\tilde X_ 1,\dots,\tilde X_ n\) such that \(\sup_ x| P(M_ n^{(k)}\leq x)- P(\tilde M_ n^{(k)}\leq x)|\to 0\) as \(n\to\infty\) for \(0\leq k\leq r\) where \(\tilde M_ n^{(k)}\) are order statistics of \(\tilde X_ 1,\dots,\tilde X_ n\). Convergence of all order statistics is also considered.
Mathematics Subject Classification ID: 60G10
zbMATH DE Number: 203256
zbMATH Keywords: stationary sequence
zbMATH Keywords: order statistics
reviewed by: Jiří Anděl
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 203256