Consistency of the frequency domain bootstrap for differentiable functionals

Patrice Bertail; Anna E. Dudek

doi:10.1214/20-EJS1787

Consistency of the frequency domain bootstrap for differentiable functionals

Patrice Bertail, Anna E. Dudek

Research output: Contribution to journal › Article › peer-review

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)
Pages (from-to)	1-36
Number of pages	36
Journal	Electronic Journal of Statistics
Volume	15
Issue number	1
DOIs	https://doi.org/10.1214/20-EJS1787
State	Published - Jan 6 2021
Externally published	Yes

ASJC Scopus subject areas

Statistics and Probability

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10.1214/20-EJS1787

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title = "Consistency of the frequency domain bootstrap for differentiable functionals",

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 Fr{\'e}chet 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.",

author = "Patrice Bertail and Dudek, {Anna E.}",

note = "KAUST Repository Item: Exported on 2022-06-14 Acknowledged 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.",

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doi = "10.1214/20-EJS1787",

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N1 - KAUST Repository Item: Exported on 2022-06-14 Acknowledged 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.

PY - 2021/1/6

Y1 - 2021/1/6

N2 - 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.

AB - 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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UR - https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-15/issue-1/Consistency-of-the-Frequency-Domain-Bootstrap-for-differentiable-functionals/10.1214/20-EJS1787.full

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EP - 36

JO - Electronic Journal of Statistics

JF - Electronic Journal of Statistics

IS - 1

ER -

Consistency of the frequency domain bootstrap for differentiable functionals

Abstract

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