Open Access
2021 Consistency of the Frequency Domain Bootstrap for differentiable functionals
Patrice Bertail, Anna E. Dudek
Electron. J. Statist. 15(1): 1-36 (2021). DOI: 10.1214/20-EJS1787


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 and Hadamard differentiability of functionals of spectral measures are defined in the time domain. 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. As an illustration the notions of quantile and range in the time domain are discussed. A simulation study is provided, in which performance of the FDB is analyzed.


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Patrice Bertail. Anna E. Dudek. "Consistency of the Frequency Domain Bootstrap for differentiable functionals." Electron. J. Statist. 15 (1) 1 - 36, 2021.


Received: 1 November 2019; Published: 2021
First available in Project Euclid: 6 January 2021

Digital Object Identifier: 10.1214/20-EJS1787

Primary: 62F40 , 62G09
Secondary: 62G20

Keywords: bootstrap , empirical process , Fréchet differentiability , influence function , second order correctness , spectral density function , spectral measure

Vol.15 • No. 1 • 2021
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