The Annals of Statistics

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

Alexander Meister

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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.

Article information

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

Dates
First available in Project Euclid: 13 May 2011

Permanent link to this document
https://projecteuclid.org/euclid.aos/1305292043

Digital Object Identifier
doi:10.1214/10-AOS872

Mathematical Reviews number (MathSciNet)
MR2850209

Zentralblatt MATH identifier
1221.62011

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

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

Citation

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. https://projecteuclid.org/euclid.aos/1305292043


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