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

TL;DR

This paper introduces a partial least squares method for estimating function-on-function regression models, addressing instability and computational issues of existing techniques, and demonstrates its effectiveness through simulations and real data analysis.

Contribution

The paper proposes a novel partial least squares approach for stable and efficient estimation in function-on-function regression models, improving upon existing methods.

Findings

Performs favorably compared to existing methods

Reduces computational time significantly

Effective in high-dimensional functional data

Abstract

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.