Abstract
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.
Original language | English (US) |
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Pages (from-to) | 1-36 |
Number of pages | 36 |
Journal | Electronic Journal of Statistics |
Volume | 15 |
Issue number | 1 |
DOIs | |
State | Published - Jan 6 2021 |
Externally published | Yes |
Bibliographical note
KAUST Repository Item: Exported on 2022-06-14Acknowledged KAUST grant number(s): OSR-2019-CRG8-4057.2
Acknowledgements: Anna Dudek acknowledges support from the King Abdullah University of Science and Technology (KAUST) Research Grant OSR-2019-CRG8-4057.2. Research of Patrice Bertail has been conducted as part of the project Labex MME-DII (ANR11-LBX-0023-01).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
ASJC Scopus subject areas
- Statistics and Probability