Additive Function-on-Function Regression. Issue 1 (2nd January 2018)

• Record Type: Journal Article
• Authors: Kim, Janet S.; Staicu, Ana-Maria; Maity, Arnab; Carroll, Raymond J.; Ruppert, David
• Is Part Of: Journal of computational and graphical statistics. Volume 27:Issue 1(2018)
• Page Start: 234
• Page End: 244
• Publication Date: 2018-01-02
• Subjects: Eigenbasis -- Functional data analysis -- Nonlinear models -- Orthogonal projection -- Penalized B-splines -- Prediction; Mathematical statistics -- Data processing -- Periodicals; Mathematical statistics -- Graphic methods -- Periodicals; 519.50285
• DOI: 10.1080/10618600.2017.1356730
• Languages: English
• ISSNs: 1061-8600

Abstract

ABSTRACT: 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.