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June 2011 Asymptotic equivalence of functional linear regression and a white noise inverse problem
Alexander Meister
Ann. Statist. 39(3): 1471-1495 (June 2011). DOI: 10.1214/10-AOS872

Abstract

We consider the statistical experiment of functional linear regression (FLR). Furthermore, we introduce a white noise model where one observes an Itô process, which contains the covariance operator of the corresponding FLR model in its construction. We prove asymptotic equivalence of FLR and this white noise model in LeCam’s sense under known design distribution. Moreover, we show equivalence of FLR and an empirical version of the white noise model for finite sample sizes. As an application, we derive sharp minimax constants in the FLR model which are still valid in the case of unknown design distribution.

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Alexander Meister. "Asymptotic equivalence of functional linear regression and a white noise inverse problem." Ann. Statist. 39 (3) 1471 - 1495, June 2011. https://doi.org/10.1214/10-AOS872

Information

Published: June 2011
First available in Project Euclid: 13 May 2011

zbMATH: 1221.62011
MathSciNet: MR2850209
Digital Object Identifier: 10.1214/10-AOS872

Subjects:
Primary: 62B15 , 62J05

Keywords: Functional data analysis , LeCam equivalence , nonparametric statistics , Statistical inverse problems , White noise model

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.39 • No. 3 • June 2011
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