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May 2018 Smooth backfitting for additive modeling with small errors-in-variables, with an application to additive functional regression for multiple predictor functions
Kyunghee Han, Hans-Georg Müller, Byeong U. Park
Bernoulli 24(2): 1233-1265 (May 2018). DOI: 10.3150/16-BEJ898

Abstract

We study smooth backfitting when there are errors-in-variables, which is motivated by functional additive models for a functional regression model with a scalar response and multiple functional predictors that are additive in the functional principal components of the predictor processes. The development of a new smooth backfitting technique for the estimation of the additive component functions in functional additive models with multiple functional predictors requires to address the difficulty that the eigenfunctions and therefore the functional principal components of the predictor processes, which are the arguments of the proposed additive model, are unknown and need to be estimated from the data. The available estimated functional principal components contain an error that is small for large samples but nevertheless affects the estimation of the additive component functions. This error-in-variables situation requires to develop new asymptotic theory for smooth backfitting. Our analysis also pertains to general situations where one encounters errors in the predictors for an additive model, when the errors become smaller asymptotically. We also study the finite sample properties of the proposed method for the application in functional additive regression through a simulation study and a real data example.

Citation

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Kyunghee Han. Hans-Georg Müller. Byeong U. Park. "Smooth backfitting for additive modeling with small errors-in-variables, with an application to additive functional regression for multiple predictor functions." Bernoulli 24 (2) 1233 - 1265, May 2018. https://doi.org/10.3150/16-BEJ898

Information

Received: 1 January 2016; Revised: 1 June 2016; Published: May 2018
First available in Project Euclid: 21 September 2017

zbMATH: 06778364
MathSciNet: MR3706793
Digital Object Identifier: 10.3150/16-BEJ898

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability

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Vol.24 • No. 2 • May 2018
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