The Annals of Statistics

Asymptotic equivalence of functional linear regression and a white noise inverse problem

Alexander Meister

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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.

Article information

Ann. Statist., Volume 39, Number 3 (2011), 1471-1495.

First available in Project Euclid: 13 May 2011

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Zentralblatt MATH identifier

Primary: 62B15: Theory of statistical experiments 62J05: Linear regression

Functional data analysis LeCam equivalence nonparametric statistics statistical inverse problems white noise model


Meister, Alexander. Asymptotic equivalence of functional linear regression and a white noise inverse problem. Ann. Statist. 39 (2011), no. 3, 1471--1495. doi:10.1214/10-AOS872.

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