The multiple hybrid bootstrap - Resampling multivariate linear processes

Jentsch, Carsten ; Kreiss, Jens-Peter

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Document Type: Article
Year of publication: 2010
The title of a journal, publication series: Journal of Multivariate Analysis : JMVA
Volume: 101
Issue number: 10
Page range: 2320-2345
Place of publication: Amsterdam [u.a.]
Publishing house: Elsevier
ISSN: 0047-259X
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Publication language: English
Institution: School of Law and Economics > Statistik (Mammen)
Subject: 510 Mathematics
Classification: MSC: 62G09 ; 62M10 ; 62H12,
Keywords (English): Frequency domain bootstrap ; Multivariate bootstrap ; Multivariate linear time series ; Kernel estimators ; Discrete Fourier transform ; Cholesky decomposition ; Spectral density matrix ; Autocovariance matrix ; Sample mean
Abstract: The paper reconsiders the autoregressive aided periodogram bootstrap (AAPB) which has been suggested in Kreiss and Paparoditis (2003) [18]. Their idea was to combine a time domain parametric and a frequency domain nonparametric bootstrap to mimic not only a part but as much as possible the complete covariance structure of the underlying time series. We extend the AAPB in two directions. Our procedure explicitly leads to bootstrap observations in the time domain and it is applicable to multivariate linear processes, but agrees exactly with the AAPB in the univariate case, when applied to functionals of the periodogram. The asymptotic theory developed shows validity of the multiple hybrid bootstrap procedure for the sample mean, kernel spectral density estimates and, with less generality, for autocovariances.

Dieser Eintrag ist Teil der Universitätsbibliographie.

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