Minimax prediction for functional linear regression with functional responses in reproducing kernel Hilbert spaces
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
Author(s)
Detail(s)
Original language | English |
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Pages (from-to) | 395-402 |
Journal / Publication | Journal of Multivariate Analysis |
Volume | 140 |
Publication status | Published - 1 Sept 2015 |
Externally published | Yes |
Link(s)
Abstract
In this article, we consider convergence rates in functional linear regression with functional responses, where the linear coefficient lies in a reproducing kernel Hilbert space (RKHS). Without assuming that the reproducing kernel and the covariate covariance kernel are aligned, convergence rates in prediction risk are established. The corresponding lower bound in rates is derived by reducing to the scalar response case. Simulation studies and two benchmark datasets are used to illustrate that the proposed approach can significantly outperform the functional PCA approach in prediction.
Research Area(s)
- Functional data, Functional response, Minimax convergence rate, Regularization
Citation Format(s)
Minimax prediction for functional linear regression with functional responses in reproducing kernel Hilbert spaces. / Lian, Heng.
In: Journal of Multivariate Analysis, Vol. 140, 01.09.2015, p. 395-402.
In: Journal of Multivariate Analysis, Vol. 140, 01.09.2015, p. 395-402.
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review