Nonparametric estimation in functional linear model
We consider the problem of estimating the slope parameter in functional linear regression, where scalar responses Y 1 yYn nare modeled in dependence of random functions X 1 X n. In the case of second order stationary random functions and as well in the non stationary case estimators of the functiona...
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| Main Author: | |
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| Format: | Chapter/Article |
| Language: | English |
| Published: |
2008
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| In: |
Functional and operatorial statistics
Year: 2008, Pages: 215-221 |
| DOI: | 10.1007/978-3-7908-2062-1_33 |
| Online Access: | Resolving-System, Volltext: http://dx.doi.org/10.1007/978-3-7908-2062-1_33 Verlag, Volltext: https://link.springer.com/chapter/10.1007/978-3-7908-2062-1_33 
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| Author Notes: | Jan Johannes |
| Summary: | We consider the problem of estimating the slope parameter in functional linear regression, where scalar responses Y 1 yYn nare modeled in dependence of random functions X 1 X n. In the case of second order stationary random functions and as well in the non stationary case estimators of the functional slope parameter and its derivatives are constructed based on a regularized inversion of the estimated covariance operator. In this paper the rate of convergence of the estimator is derived assuming that the slope parameter belongs to the well-known Sobolev space of periodic functions and that the covariance operator is finitely, infinitely or in some general form smoothing. |
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| Item Description: | Gesehen am 19.07.2018 |
| Physical Description: | Online Resource |
| ISBN: | 9783790820621 |
| DOI: | 10.1007/978-3-7908-2062-1_33 |