Abstract
We propose a functional version of the Hodrick–Prescott filter for functional data which take values in an infinite-dimensional separable Hilbert space. We further characterize the associated optimal smoothing operator when the associated linear operator is compact and the underlying distribution of the data is Gaussian.
Funding statement: Financial support from the Swedish Export Corporation (SEK) is gratefully acknowledge.
Acknowledgements
We would like to thank the referee for his careful reading of the paper and his insightful remarks that helped improve its content.
References
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© 2017 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- A functional Hodrick–Prescott filter
- On the peakon inverse problem for the Degasperis–Procesi equation
- Recovery of harmonic functions from partial boundary data respecting internal pointwise values
- Inverse spectral problems of transmission eigenvalue problem for anisotropic media with spherical symmetry assumptions
- An inverse problem for a nonlinear diffusion equation with time-fractional derivative
- Imaging of complex-valued tensors for two-dimensional Maxwell’s equations
- Direct and inverse source problems for a space fractional advection dispersion equation
- A conditional Lipschitz stability for determining a space-dependent source coefficient in the 2D/3D advection-dispersion equation
- Inverse transmission eigenvalue problems with the twin-dense nodal subset
- Stability of the inverse boundary value problem for the biharmonic operator: Logarithmic estimates
Artikel in diesem Heft
- Frontmatter
- A functional Hodrick–Prescott filter
- On the peakon inverse problem for the Degasperis–Procesi equation
- Recovery of harmonic functions from partial boundary data respecting internal pointwise values
- Inverse spectral problems of transmission eigenvalue problem for anisotropic media with spherical symmetry assumptions
- An inverse problem for a nonlinear diffusion equation with time-fractional derivative
- Imaging of complex-valued tensors for two-dimensional Maxwell’s equations
- Direct and inverse source problems for a space fractional advection dispersion equation
- A conditional Lipschitz stability for determining a space-dependent source coefficient in the 2D/3D advection-dispersion equation
- Inverse transmission eigenvalue problems with the twin-dense nodal subset
- Stability of the inverse boundary value problem for the biharmonic operator: Logarithmic estimates