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2016 Functional wavelet regression for linear function-on-function models
Ruiyan Luo, Xin Qi, Yanhong Wang
Electron. J. Statist. 10(2): 3179-3216 (2016). DOI: 10.1214/16-EJS1204

Abstract

We consider linear function-on-function regression models with multiple predictive curves. We first apply the wavelet transformation to the predictive curves and transform the original model to a linear model with functional response and high dimensional multivariate predictors. Based on the best finite dimensional approximation to the signal part in the response curve, we find an expansion of the vector of coefficient functions, which enjoys a good predictive property. To estimate this expansion, we propose a penalized generalized eigenvalue problem followed by a penalized least squares problem. We establish the sparse oracle inequalities for our estimates in the high-dimensional settings. The choices of tuning parameters and the number of components are provided. Simulations studies and application to real datasets demonstrate that our method has good predictive performance and is efficient in dimension reduction.

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Ruiyan Luo. Xin Qi. Yanhong Wang. "Functional wavelet regression for linear function-on-function models." Electron. J. Statist. 10 (2) 3179 - 3216, 2016. https://doi.org/10.1214/16-EJS1204

Information

Received: 1 March 2016; Published: 2016
First available in Project Euclid: 12 November 2016

zbMATH: 1353.62073
MathSciNet: MR3571966
Digital Object Identifier: 10.1214/16-EJS1204

Subjects:
Primary: 62J05

Keywords: Function-on-function regression , generalized eigenvalue problem , penalized least squares problem , signal compression , wavelet transformation

Rights: Copyright © 2016 The Institute of Mathematical Statistics and the Bernoulli Society

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Vol.10 • No. 2 • 2016
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