Journal
JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS
Volume 27, Issue 1, Pages 234-244Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/10618600.2017.1356730
Keywords
Eigenbasis; Functional data analysis; Nonlinear models; Orthogonal projection; Penalized B-splines; Prediction
Categories
Funding
- National Institutes of Health [R00 ES017744, R01 MH086633, R01 NS085211, AST 1312903, DMS 1454942, U01-CA057030]
- North Carolina State University [Faculty Research & Professional Development]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1454942] Funding Source: National Science Foundation
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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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