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- Title
Optimal risk rate in a functional inverse problem.
- Authors
Pang, Johnny; Ruymgaart, Frits
- Abstract
In this note, we will consider the problem of recovering an unknown input function when the output function is observed in its entirety, blurred with functional error. An estimator is constructed whose risk converges at an optimal rate. In this functional model, convergence rates of order 1/ n ( n is the sample size) are possible, provided that the error distribution is sufficiently concentrated so as to compensate for the ill-posedness of the inverse of the model operator.
- Subjects
INVERSION (Geophysics); CONVERGENT evolution; BIOLOGY; PHYLOGENY; BIOLOGICAL evolution
- Publication
Statistica Neerlandica, 2012, Vol 66, Issue 2, p111
- ISSN
0039-0402
- Publication type
Article
- DOI
10.1111/j.1467-9574.2011.00498.x