Additive Function-on-Function Regression

作者：Kim Janet S; Staicu Ana Maria^*; Maity Arnab; Carroll Raymond J; Ruppert David

来源：Journal of Computational and Graphical Statistics, 2018, 27(1): 234-244.

DOI：10.1080/10618600.2017.1356730

• Eigenbasis
• Functional data analysis
• Nonlinear models
• Orthogonal projection
• Penalized B-splines
• Prediction

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.

• 出版日期2018