Extremes of projections of functional time series on data-driven basis systems
type: Item
instance of: scholarly article
title: Extremes of projections of functional time series on data-driven basis systems
zbMATH Open document ID: 1398.62235
author: Qian Xiong
author: Piotr Kokoszka
published in: Extremes
publication date: 2018-08-03T00:00:00Z
review text: In this manuscript the authors consider a problem of derivation under what conditions the vectors \(\widehat{\mathbf Z}_i=[\widehat{Z}_{i1},\widehat{Z}_{i2},\dots,\widehat{Z}_{ip}]'\), \(1\leq i\leq N\), have the same asymptotic extreme behavior as the unobservable vectors \(\mathbf Z_i=[Z_{i1},Z_{i2},\dots,Z_{ip}]'\) as \(N\) tends to \(\infty\). The elements \(\widehat{Z}_{ij}\) are the estimated scores and appear in the expansion \(X_i(t)\approx \sum_{j=1}^p \widehat{\lambda}_{j}^{1/2} \widehat{Z}_{ij} \widehat{v}_j(t)\), where \(X_i\) is a function in the space \(L^2\) of a strictly stationary mean zero time series \(\{X_i\}\). The convergence in distribution of extremes of the random variables \(\langle {X_i},{v_j}\rangle\) and \(\langle {X_i},{\widehat{v}_j}\rangle\) are derived under general assumptions and the rates of convergence of their distribution functions are considered.
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 62G32
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 62H25
zbMATH DE Number: 6912881
zbMATH Keywords: extreme values
zbMATH Keywords: functional data
zbMATH Keywords: Gumbel distribution
zbMATH Keywords: time series
reviewed by: Miroslav M. Ristić
describes a project that uses: fda (R)
describes a project that uses: freqdom.fda
MaRDI profile type: Publication
full work available at URL: s10687-017-0302-8
OpenAlex ID: W2742387330
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DOI: 10.1007/S10687-017-0302-8
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description: scientific article; zbMATH DE number 6912881