Asymptotic test for independence of extreme values
type: Item
instance of: scholarly article
title: Asymptotic test for independence of extreme values
zbMATH Open document ID: 0792.62040
DOI: 10.1007/BF01874654
author: E. S. Miasaki
author: Chang C. Y. Dorea
published in: Acta Mathematica Hungarica
publication date: 1994-07-26T00:00:00Z
review text: Let \((X_ 1,Y_ 1),(X_ 2,Y_ 2),\dots\) be a sequence of independent random vectors with a common distribution \(L\) with marginal \(R\) and \(S\) (in short, we write \(L\in{\mathcal M}(R,S))\). Let \(R\) and \(S\) be such that with suitable norming constants \(a_ n\), \(b_ n\), \(c_ n\) and \(d_ n\) the random variables \[ X(n)= (\max \{X_ 1,\dots,X_ n\}- b_ n)a_ n^{-1} \qquad \text{and} \qquad Y(n)= (\max \{Y_ 1,\dots,Y_ n\}- c_ n)d_ n^{-1} \] have nondegenerate limiting distributions \(G\) and \(H\), respectively. Assuming that \((X(n),Y(n))\) converges in distribution to some \(F\in {\mathcal M}(G,H)\) we study conditions that will assure \(F=GH\).
Mathematics Subject Classification ID: 62G10
Mathematics Subject Classification ID: 62G30
Mathematics Subject Classification ID: 62G20
zbMATH DE Number: 575889
zbMATH Keywords: asymptotic test
zbMATH Keywords: independence of extreme values
zbMATH Keywords: nondegenerate limiting distributions
MaRDI profile type: Publication
cites work: Estimation of the extreme value and the extreme points
cites work: Bivariate CDF iterations and asymptotic independence
cites work: Q4162318
cites work: Estimation of Parameters and Larger Quantiles Based on the k Largest Observations
full work available at URL: https://doi.org/10.1007/bf01874654
OpenAlex ID: W2027740154
description: scientific article; zbMATH DE number 575889