Consistency of the Frequency Domain Bootstrap for differentiable functionals

In this paper consistency of the Frequency Domain Bootstrap for differentiable functionals of spectral density function of a linear stationary time series is discussed. The notion of influence function in the time domain on spectral measures is introduced. Moreover, the Fréchet differen-tiability of...

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Bibliographic Details
Published inElectronic journal of statistics Vol. 15; no. 1; pp. 1 - 36
Main Authors Bertail, Patrice, Dudek, Anna E.
Format Journal Article
LanguageEnglish
Published Shaker Heights, OH : Institute of Mathematical Statistics 01.01.2021
Subjects
Mathematics
Statistics
Fréchet differentiability
influ- ence function
second order correctness
empirical process
spectral density function
bootstrap
influence function
spectral measure
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Summary:In this paper consistency of the Frequency Domain Bootstrap for differentiable functionals of spectral density function of a linear stationary time series is discussed. The notion of influence function in the time domain on spectral measures is introduced. Moreover, the Fréchet differen-tiability of functionals of spectral measures is defined. Sufficient and necessary conditions for consistency of the FDB in the considered problems are provided and the second order correctness is discussed for some functionals. Finally, validity of the FDB for the empirical processes is considered.
ISSN:1935-7524
1935-7524
DOI:10.1214/20-EJS1787