Thresholding projection estimators in functional linear models

• Verfasst von: Cardot, Hervé [VerfasserIn]
• Verfasst von: Johannes, Jan [VerfasserIn]
• Titel: Thresholding projection estimators in functional linear models
• Verf.angabe: Hervé Cardot, Jan Johannes
• Jahr des Originals: 2009
• Umfang: 14 S.
• Fussnoten: Available online 24 March 2009 ; Gesehen am 19.07.2018
• Titel Quelle: Enthalten in: Journal of multivariate analysis
• Jahr Quelle: 2010
• Band/Heft Quelle: 101(2010), 2, S. 395-408
• ISSN Quelle: 1095-7243
• DOI: doi:10.1016/j.jmva.2009.03.001
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1577777174

Abstract

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.