Continuously additive models for nonlinear functional regression

Müller, Hans‐Georg; Wu, Yichao; Yao, Fang

doi:10.1093/biomet/ast004

Cited by 56 publications

(38 citation statements)

References 28 publications

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“…Additive models allow nonparametric modeling of the relationship between the response and the predictors while avoiding the so-called curse of dimensionality and being easily interpreted. Additive and generalized additive models for a scalar response and functional predictors were introduced by McLean et al (2014) and Müller et al (2013).…”

Section: Introductionmentioning

confidence: 99%

Additive Function-on-Function Regression

Kim

Staicu

Maity

et al. 2018

Journal of Computational and Graphical Statistics

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We study additive function-on-function regression where the mean response at a particular time point depends on the time point itself, as well as the entire covariate trajectory. We develop a computationally efficient estimation methodology based on a novel combination of spline bases with an eigenbasis to represent the trivariate kernel function. We discuss prediction of a new response trajectory, propose an inference procedure that accounts for total variability in the predicted response curves, and construct pointwise prediction intervals. The estimation/inferential procedure accommodates realistic scenarios, such as correlated error structure as well as sparse and/or irregular designs. We investigate our methodology in finite sample size through simulations and two real data applications. Supplementary Material for this article is available online.

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Section: Introductionmentioning

confidence: 99%

Additive Function-on-Function Regression

Kim

Staicu

Maity

et al. 2018

Journal of Computational and Graphical Statistics

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“…Recently McLean, Hooker, and Ruppert (2014) proposed a restricted likelihood ratio test for testing for linear dependence between a scalar response and a functional covariate, in the class of functional generalized additive models (Mclean, Hooker, Staicu, Scheipl, and Ruppert 2014; Müller, Wu, and Yao 2013). In what follows, we write ∫ X i ( t ) β ( t ) dt instead of ∫ 𝒯 X i ( t ) β ( t ) dt for notational convenience.…”

Section: Methodsmentioning

confidence: 99%

Classical testing in functional linear models

Kong

Staicu

Maity

2016

Journal of Nonparametric Statistics

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We extend four tests common in classical regression - Wald, score, likelihood ratio and F tests - to functional linear regression, for testing the null hypothesis, that there is no association between a scalar response and a functional covariate. Using functional principal component analysis, we re-express the functional linear model as a standard linear model, where the effect of the functional covariate can be approximated by a finite linear combination of the functional principal component scores. In this setting, we consider application of the four traditional tests. The proposed testing procedures are investigated theoretically for densely observed functional covariates when the number of principal components diverges. Using the theoretical distribution of the tests under the alternative hypothesis, we develop a procedure for sample size calculation in the context of functional linear regression. The four tests are further compared numerically for both densely and sparsely observed noisy functional data in simulation experiments and using two real data applications.

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“…The single-index model has been extended to multiple-index model (James and Silverman, 2005;Chen et al, 2011;Ferraty et al, 2013) with multiple linear functionals of the single predictor: Müller et al (2013) and McLean et al (2014) proposed the continuously additive model y = µ + ∫ I F (X(s), s)ds + ε, where…”

Section: X(s)β(s)ds ) + ε the Coefficient Function β(·) And The Unspmentioning

confidence: 99%