Additive Function-on-Function Regression

Publication Type:
Journal Article
Journal of Computational and Graphical Statistics, 2018, 27 (1), pp. 234 - 244
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© 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.
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