Additive Function-on-Function Regression Academic Article uri icon

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.

author list (cited authors)

  • Kim, J. S., Staicu, A., Maity, A., Carroll, R. J., & Ruppert, D.

citation count

  • 11

publication date

  • January 2018