# Additive Function-on-Function Regression

arXiv: https://arxiv.org/abs/1606.03775 · HTML: https://mlsanity.com/paper/1606.03775/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2016.

## Built on by (most cited first, 3 of 3)

- [Modern Non-Linear Function-on-Function Regression](https://mlsanity.com/paper/2107.14151/) (2021)
- [Error-in-variables modelling for operator learning](https://mlsanity.com/paper/2204.10909/) (2022)
- [Deep Gaussian Processes for Functional Maps](https://mlsanity.com/paper/2510.22068/) (2025)

## Abstract (arXiv)

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.