On the asymptotic locations of the largest and smallest extremes of a stationary sequence
type: Item
instance of: scholarly article
title: On the asymptotic locations of the largest and smallest extremes of a stationary sequence
zbMATH Open document ID: 1434.60132
author: Luisa Pereira
published in: Journal of Theoretical Probability
publication date: 2018-08-16T00:00:00Z
review text: This article deals with the asymptotic joint locations of the \(k\)-th largest and the \(r\)-th smallest order statistics of a stationary sequence of random variables. It is shown under some conditions, that the upper and lower order statistics are asymptotically independent, by showing that the corresponding limiting point processes are couplings of independent compound Poisson point processes. The asymptotic joint distribution of the locations of the \(k\)-th largest and \(r\)-th smallest extremes are obtained and it is shown that, under some conditions, the locations vector of the \(k\)-th upper order statistics and the locations vector of the \(r\)-th lower order statistics are asymptotically independent. The results are extensions of the results in [\textit{L. Pereira} and \textit{H. Ferreira}, J. Stat. Plann. Inference 104, No. 2, 287--295 (2002; Zbl 0998.60047)], for the sequences of partial maximum and minimum and their locations.
Mathematics Subject Classification ID: 60G70
Mathematics Subject Classification ID: 60G55
zbMATH DE Number: 6919751
zbMATH Keywords: order statistics
zbMATH Keywords: exceedances
zbMATH Keywords: locations of extremes
zbMATH Keywords: dependence conditions
zbMATH Keywords: point processes
zbMATH Keywords: asymptotic independence
reviewed by: Sreenivasan Ravi
MaRDI profile type: Publication
full work available at URL: s10959-017-0742-8
OpenAlex ID: W2593857586
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DOI: 10.1007/S10959-017-0742-8
description: scientific article; zbMATH DE number 6919751