# On function-on-function regression: Partial least squares approach

arXiv: https://arxiv.org/abs/1912.06995 · HTML: https://mlsanity.com/paper/1912.06995/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Dec 2019.

## Built on by (most cited first, 2 of 2)

- [FAStEN: An Efficient Adaptive Method for Feature Selection and Estimation in High-Dimensional Functional Regressions](https://mlsanity.com/paper/2303.14801/) (2023)
- [Deep Gaussian Processes for Functional Maps](https://mlsanity.com/paper/2510.22068/) (2025)

## Abstract (arXiv)

Functional data analysis tools, such as function-on-function regression models, have received considerable attention in various scientific fields because of their observed high-dimensional and complex data structures. Several statistical procedures, including least squares, maximum likelihood, and maximum penalized likelihood, have been proposed to estimate such function-on-function regression models. However, these estimation techniques produce unstable estimates in the case of degenerate functional data or are computationally intensive. To overcome these issues, we proposed a partial least squares approach to estimate the model parameters in the function-on-function regression model. In the proposed method, the B-spline basis functions are utilized to convert discretely observed data into their functional forms. Generalized cross-validation is used to control the degrees of roughness. The finite-sample performance of the proposed method was evaluated using several Monte-Carlo simulations and an empirical data analysis. The results reveal that the proposed method competes favorably with existing estimation techniques and some other available function-on-function regression models, with significantly shorter computational time.