  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.
