Nonparametric estimation in functional linear model
(2008) Functional and Operatorial Statistics — ISBN: [978-3-7908-2062-1], p. 215-221, published
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- Abstract
- 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.
- Affiliations
Universitat Heidelberg Institut für Angewandte Mathematik
Citations
Johannes, J. (2008). Nonparametric estimation in functional linear model. In Dabo-Niang, Sophie; Ferraty, Frédéric (ed.), Functional and Operatorial Statistics (p. p. 215-221). Springer. https://doi.org/10.1007/978-3-7908-2062-1_33