Nonparametric estimation in functional linear model

• Verfasst von: Johannes, Jan [VerfasserIn]
• Titel: Nonparametric estimation in functional linear model
• Verf.angabe: Jan Johannes
• Umfang: 7 S.
• Fussnoten: Gesehen am 19.07.2018
• Titel Quelle: Enthalten in: Functional and Operatorial Statistics
• Jahr Quelle: 2008
• Band/Heft Quelle: (2008), S. 215-221
• ISBN Quelle: 978-3-7908-2062-1
• DOI: doi:10.1007/978-3-7908-2062-1_33
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1577778057

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.