Bernoulli

  • Bernoulli
  • Volume 24, Number 2 (2018), 1233-1265.

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, and Byeong U. Park

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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.

Article information

Source
Bernoulli, Volume 24, Number 2 (2018), 1233-1265.

Dates
Received: January 2016
Revised: June 2016
First available in Project Euclid: 21 September 2017

Permanent link to this document
https://projecteuclid.org/euclid.bj/1505980895

Digital Object Identifier
doi:10.3150/16-BEJ898

Mathematical Reviews number (MathSciNet)
MR3706793

Zentralblatt MATH identifier
06778364

Keywords
errors in predictors functional additive model functional data analysis functional principal component kernel smoothing smooth backfitting

Citation

Han, Kyunghee; Müller, Hans-Georg; Park, Byeong U. Smooth backfitting for additive modeling with small errors-in-variables, with an application to additive functional regression for multiple predictor functions. Bernoulli 24 (2018), no. 2, 1233--1265. doi:10.3150/16-BEJ898. https://projecteuclid.org/euclid.bj/1505980895


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