Thresholding projection estimators in functional linear models
We consider the problem of estimating the regression function in functional linear regression models by proposing a new type of projection estimators which combine dimension reduction and thresholding. The introduction of a threshold rule allows us to get consistency under broad assumptions as well...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2010
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| In: |
Journal of multivariate analysis
Year: 2009, Volume: 101, Issue: 2, Pages: 395-408 |
| ISSN: | 1095-7243 |
| DOI: | 10.1016/j.jmva.2009.03.001 |
| Online Access: | Verlag, kostenfrei, Volltext: http://dx.doi.org/10.1016/j.jmva.2009.03.001 Verlag, kostenfrei, Volltext: http://www.sciencedirect.com/science/article/pii/S0047259X09000608 
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| Author Notes: | Hervé Cardot, Jan Johannes |
MARC
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| 520 | |a We consider the problem of estimating the regression function in functional linear regression models by proposing a new type of projection estimators which combine dimension reduction and thresholding. The introduction of a threshold rule allows us to get consistency under broad assumptions as well as minimax rates of convergence under additional regularity hypotheses. We also consider the particular case of Sobolev spaces generated by the trigonometric basis which permits us to get easily mean squared error of prediction as well as estimators of the derivatives of the regression function. We prove that these estimators are minimax and rates of convergence are given for some particular cases. | ||
| 534 | |c 2009 | ||
| 650 | 4 | |a Derivatives estimation | |
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| 650 | 4 | |a Hilbert scale | |
| 650 | 4 | |a Linear inverse problem | |
| 650 | 4 | |a Mean squared error of prediction | |
| 650 | 4 | |a Optimal rate of convergence | |
| 650 | 4 | |a Sobolev space | |
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