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Article Dans Une Revue Electronic Journal of Statistics Année : 2021

Consistency of the Frequency Domain Bootstrap for differentiable functionals

Résumé

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.
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Dates et versions

hal-02385774 , version 1 (29-11-2019)
hal-02385774 , version 2 (11-12-2020)
hal-02385774 , version 3 (06-01-2021)

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Citer

Patrice Bertail, Anna Dudek. Consistency of the Frequency Domain Bootstrap for differentiable functionals. Electronic Journal of Statistics , 2021, 14 (1), pp.1-36. ⟨10.1214/20-EJS1787⟩. ⟨hal-02385774v3⟩
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