Additive Function-on-Function Regression

Kim, JS; Staicu, AM; Maity, A; Carroll, RJ; Ruppert, D

Additive Function-on-Function Regression

Kim, JS Staicu, AM Maity, A Carroll, RJ

Ruppert, D

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Publication Type:: Journal Article
Citation:: Journal of Computational and Graphical Statistics, 2018, 27 (1), pp. 234 - 244
Issue Date:: 2018-01-02

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Field	Value	Language
dc.contributor.author	Kim, JS	en_US
dc.contributor.author	Staicu, AM	en_US
dc.contributor.author	Maity, A	en_US
dc.contributor.author	Carroll, RJ https://orcid.org/0000-0002-5465-9682	en_US
dc.contributor.author	Ruppert, D	en_US
dc.date.issued	2018-01-02	en_US
dc.identifier.citation	Journal of Computational and Graphical Statistics, 2018, 27 (1), pp. 234 - 244	en_US
dc.identifier.issn	1061-8600	en_US
dc.identifier.uri	http://hdl.handle.net/10453/128923
dc.description.abstract	© 2018 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America. 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.	en_US
dc.relation.ispartof	Journal of Computational and Graphical Statistics	en_US
dc.relation.isbasedon	10.1080/10618600.2017.1356730	en_US
dc.subject.classification	Statistics & Probability	en_US
dc.title	Additive Function-on-Function Regression	en_US
dc.type	Journal Article
utslib.citation.volume	1	en_US
utslib.citation.volume	27	en_US
utslib.for	0104 Statistics	en_US
utslib.for	1403 Econometrics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
utslib.copyright.status	closed_access
pubs.issue	1	en_US
pubs.publication-status	Published	en_US
pubs.volume	27	en_US

Abstract:

© 2018 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America. 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.

Please use this identifier to cite or link to this item:

http://hdl.handle.net/10453/128923